IXL Skill Plan | Texas Essential Knowledge and Skills (TEKS): Geometry

Texas Essential Knowledge and Skills (TEKS): Geometry

Skills available for Texas Geometry standards

Strand

Mathematical process standards
Coordinate and transformational geometry
Logical argument and constructions
Proof and congruence
Similarity, proof, and trigonometry
Two-dimensional and three-dimensional figures
Circles
Probability

Print skill plan

1	Mathematical process standards
1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.
A apply mathematics to problems arising in everyday life, society, and the workplace;		Logical argument and constructions 1. Identify hypotheses and conclusions 2. Counterexamples 3. Conditionals Proof and congruence 4. Pythagorean theorem Two-dimensional and three-dimensional figures 5. Checkpoint: Volume 6. Checkpoint: Surface area Probability 7. Probability of independent and dependent events 8. Find probabilities using combinations and permutations 9. Find conditional probabilities using two-way frequency tables
A apply mathematics to problems arising in everyday life, society, and the workplace;
Logical argument and constructions 1. Identify hypotheses and conclusions 2. Counterexamples 3. Conditionals Proof and congruence 4. Pythagorean theorem Two-dimensional and three-dimensional figures 5. Checkpoint: Volume 6. Checkpoint: Surface area Probability 7. Probability of independent and dependent events 8. Find probabilities using combinations and permutations 9. Find conditional probabilities using two-way frequency tables

B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;		Coordinate and transformational geometry 1. Reflections and rotations: write the rule 2. Classify shapes on the coordinate plane: justify your answer 3. Checkpoint: Transformations of geometric figures Logical argument and constructions 4. Triangle Inequality Theorem Proof and congruence 5. Angle diagrams: solve for the variable 6. Determine if two figures are congruent: justify your answer 7. Prove triangles are congruent using rigid motions 8. SSS Theorem in the coordinate plane 9. Proving a quadrilateral is a parallelogram 10. Classify quadrilaterals on the coordinate plane: justify your answer Similarity, proof, and trigonometry 11. Similar triangles and indirect measurement 12. Determine if two figures are similar: justify your answer 13. Checkpoint: Right triangle trigonometry Two-dimensional and three-dimensional figures 14. Perimeter and area: changes in scale 15. Surface area and volume: changes in scale Circles 16. Checkpoint: Angles and lines in circles 17. Checkpoint: Arc length and area of sectors 18. Checkpoint: Equations of circles Probability 19. Checkpoint: Probability
B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
Coordinate and transformational geometry 1. Reflections and rotations: write the rule 2. Classify shapes on the coordinate plane: justify your answer 3. Checkpoint: Transformations of geometric figures Logical argument and constructions 4. Triangle Inequality Theorem Proof and congruence 5. Angle diagrams: solve for the variable 6. Determine if two figures are congruent: justify your answer 7. Prove triangles are congruent using rigid motions 8. SSS Theorem in the coordinate plane 9. Proving a quadrilateral is a parallelogram 10. Classify quadrilaterals on the coordinate plane: justify your answer Similarity, proof, and trigonometry 11. Similar triangles and indirect measurement 12. Determine if two figures are similar: justify your answer 13. Checkpoint: Right triangle trigonometry Two-dimensional and three-dimensional figures 14. Perimeter and area: changes in scale 15. Surface area and volume: changes in scale Circles 16. Checkpoint: Angles and lines in circles 17. Checkpoint: Arc length and area of sectors 18. Checkpoint: Equations of circles Probability 19. Checkpoint: Probability

C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;		Coordinate and transformational geometry 1. Midpoint formula: find the midpoint 2. Distance formula Logical argument and constructions 3. Checkpoint: Geometric constructions Proof and congruence 4. Prove triangles are congruent using rigid motions 5. Classify quadrilaterals on the coordinate plane: justify your answer Similarity, proof, and trigonometry 6. Side lengths and angle measures in similar figures 7. Perimeters of similar figures 8. Areas of similar figures Two-dimensional and three-dimensional figures 9. Area of regular polygons 10. Surface area of spheres 11. Volume of prisms and cylinders 12. Volume of pyramids and cones Circles 13. Understand arc length and sector area of a circle 14. Derive equations of circles using the Pythagorean theorem Probability 15. Find probabilities using combinations and permutations 16. Find conditional probabilities using two-way frequency tables 17. Independence and conditional probability
C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
Coordinate and transformational geometry 1. Midpoint formula: find the midpoint 2. Distance formula Logical argument and constructions 3. Checkpoint: Geometric constructions Proof and congruence 4. Prove triangles are congruent using rigid motions 5. Classify quadrilaterals on the coordinate plane: justify your answer Similarity, proof, and trigonometry 6. Side lengths and angle measures in similar figures 7. Perimeters of similar figures 8. Areas of similar figures Two-dimensional and three-dimensional figures 9. Area of regular polygons 10. Surface area of spheres 11. Volume of prisms and cylinders 12. Volume of pyramids and cones Circles 13. Understand arc length and sector area of a circle 14. Derive equations of circles using the Pythagorean theorem Probability 15. Find probabilities using combinations and permutations 16. Find conditional probabilities using two-way frequency tables 17. Independence and conditional probability

D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;		Coordinate and transformational geometry 1. Classify congruence transformations 2. Sequences of congruence transformations: choose the sequence 3. Sequences of congruence transformations: find the rules 4. Checkpoint: Parallel and perpendicular lines Logical argument and constructions 5. Counterexamples 6. Converses, inverses, and contrapositives 7. Biconditionals 8. Truth values Proof and congruence 9. Determine if two figures are congruent: justify your answer 10. Classify quadrilaterals on the coordinate plane: justify your answer Similarity, proof, and trigonometry 11. Similarity statements 12. Similar triangles and similarity transformations 13. Determine if two figures are similar: justify your answer 14. Similarity of circles Two-dimensional and three-dimensional figures 15. Checkpoint: Cross sections and solids of revolution Circles 16. Derive equations of circles using the Pythagorean theorem Probability 17. Geometric probability
D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
Coordinate and transformational geometry 1. Classify congruence transformations 2. Sequences of congruence transformations: choose the sequence 3. Sequences of congruence transformations: find the rules 4. Checkpoint: Parallel and perpendicular lines Logical argument and constructions 5. Counterexamples 6. Converses, inverses, and contrapositives 7. Biconditionals 8. Truth values Proof and congruence 9. Determine if two figures are congruent: justify your answer 10. Classify quadrilaterals on the coordinate plane: justify your answer Similarity, proof, and trigonometry 11. Similarity statements 12. Similar triangles and similarity transformations 13. Determine if two figures are similar: justify your answer 14. Similarity of circles Two-dimensional and three-dimensional figures 15. Checkpoint: Cross sections and solids of revolution Circles 16. Derive equations of circles using the Pythagorean theorem Probability 17. Geometric probability

E create and use representations to organize, record, and communicate mathematical ideas;		Coordinate and transformational geometry 1. Partition a line segment in a given ratio 2. Equations of parallel and perpendicular lines 3. Sequences of congruence transformations: graph the image 4. Congruence transformations: mixed review Logical argument and constructions 5. Truth tables 6. Construct the midpoint or perpendicular bisector of a segment 7. Construct an angle bisector 8. Construct a congruent angle 9. Construct a perpendicular line 10. Construct parallel lines Proof and congruence 11. Proofs involving angles 12. SSS and SAS Theorems 13. ASA and AAS Theorems 14. Proving triangles congruent by SSS, SAS, ASA, and AAS 15. Proofs involving corresponding parts of congruent triangles 16. Proofs involving isosceles triangles 17. Proving a quadrilateral is a parallelogram 18. Prove the Pythagorean theorem Similarity, proof, and trigonometry 19. Similarity statements 20. Prove similarity statements 21. Prove proportions or angle congruences using similarity 22. Proofs involving similarity in right triangles Circles 23. Write equations of circles in standard form from graphs Probability 24. Find conditional probabilities using two-way frequency tables
E create and use representations to organize, record, and communicate mathematical ideas;
Coordinate and transformational geometry 1. Partition a line segment in a given ratio 2. Equations of parallel and perpendicular lines 3. Sequences of congruence transformations: graph the image 4. Congruence transformations: mixed review Logical argument and constructions 5. Truth tables 6. Construct the midpoint or perpendicular bisector of a segment 7. Construct an angle bisector 8. Construct a congruent angle 9. Construct a perpendicular line 10. Construct parallel lines Proof and congruence 11. Proofs involving angles 12. SSS and SAS Theorems 13. ASA and AAS Theorems 14. Proving triangles congruent by SSS, SAS, ASA, and AAS 15. Proofs involving corresponding parts of congruent triangles 16. Proofs involving isosceles triangles 17. Proving a quadrilateral is a parallelogram 18. Prove the Pythagorean theorem Similarity, proof, and trigonometry 19. Similarity statements 20. Prove similarity statements 21. Prove proportions or angle congruences using similarity 22. Proofs involving similarity in right triangles Circles 23. Write equations of circles in standard form from graphs Probability 24. Find conditional probabilities using two-way frequency tables

F analyze mathematical relationships to connect and communicate mathematical ideas; and		Coordinate and transformational geometry 1. Determine if a point lies on a circle Logical argument and constructions 2. Conditionals 3. Truth tables 4. Truth values Proof and congruence 5. Proving triangles congruent by SSS and SAS 6. Proving triangles congruent by ASA and AAS 7. Proving triangles congruent by SSS, SAS, ASA, and AAS 8. Proofs involving corresponding parts of congruent triangles 9. Proofs involving isosceles triangles 10. Proving a quadrilateral is a parallelogram Similarity, proof, and trigonometry 11. Similar triangles and indirect measurement 12. Similarity of circles 13. Areas of similar figures Two-dimensional and three-dimensional figures 14. Surface area and volume of similar solids Circles 15. Understand arc length and sector area of a circle 16. Perimeter of polygons with an inscribed circle 17. Angles in inscribed quadrilaterals I 18. Write equations of circles in standard form from graphs Probability 19. Identify independent events
F analyze mathematical relationships to connect and communicate mathematical ideas; and
Coordinate and transformational geometry 1. Determine if a point lies on a circle Logical argument and constructions 2. Conditionals 3. Truth tables 4. Truth values Proof and congruence 5. Proving triangles congruent by SSS and SAS 6. Proving triangles congruent by ASA and AAS 7. Proving triangles congruent by SSS, SAS, ASA, and AAS 8. Proofs involving corresponding parts of congruent triangles 9. Proofs involving isosceles triangles 10. Proving a quadrilateral is a parallelogram Similarity, proof, and trigonometry 11. Similar triangles and indirect measurement 12. Similarity of circles 13. Areas of similar figures Two-dimensional and three-dimensional figures 14. Surface area and volume of similar solids Circles 15. Understand arc length and sector area of a circle 16. Perimeter of polygons with an inscribed circle 17. Angles in inscribed quadrilaterals I 18. Write equations of circles in standard form from graphs Probability 19. Identify independent events

G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.		Coordinate and transformational geometry 1. Classify shapes on the coordinate plane: justify your answer Logical argument and constructions 2. Identify hypotheses and conclusions 3. Counterexamples 4. Biconditionals 5. Lines, line segments, and rays Proof and congruence 6. Checkpoint: Line and angle theorems 7. Checkpoint: Parallelogram theorems 8. Checkpoint: Rigid motion and congruence 9. Checkpoint: Triangle theorems Similarity, proof, and trigonometry 10. Checkpoint: Triangle similarity and congruence Two-dimensional and three-dimensional figures 11. Checkpoint: Cross sections and solids of revolution Probability 12. Identify independent and dependent events
G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Coordinate and transformational geometry 1. Classify shapes on the coordinate plane: justify your answer Logical argument and constructions 2. Identify hypotheses and conclusions 3. Counterexamples 4. Biconditionals 5. Lines, line segments, and rays Proof and congruence 6. Checkpoint: Line and angle theorems 7. Checkpoint: Parallelogram theorems 8. Checkpoint: Rigid motion and congruence 9. Checkpoint: Triangle theorems Similarity, proof, and trigonometry 10. Checkpoint: Triangle similarity and congruence Two-dimensional and three-dimensional figures 11. Checkpoint: Cross sections and solids of revolution Probability 12. Identify independent and dependent events

2-3	Coordinate and transformational geometry
2 The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures.
A determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint;		1. Midpoints 2. Midpoint formula: find the midpoint 3. Partition a line segment in a given ratio
A determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint;
1. Midpoints 2. Midpoint formula: find the midpoint 3. Partition a line segment in a given ratio

B derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines; and		1. Midpoint formula: find the midpoint 2. Distance formula 3. Slopes of lines 4. Slopes of parallel and perpendicular lines 5. Classify shapes on the coordinate plane: justify your answer 6. Determine if a point lies on a circle
B derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines; and
1. Midpoint formula: find the midpoint 2. Distance formula 3. Slopes of lines 4. Slopes of parallel and perpendicular lines 5. Classify shapes on the coordinate plane: justify your answer 6. Determine if a point lies on a circle

C determine an equation of a line parallel or perpendicular to a given line that passes through a given point.		1. Equations of parallel and perpendicular lines
C determine an equation of a line parallel or perpendicular to a given line that passes through a given point.
1. Equations of parallel and perpendicular lines

Checkpoint opportunity		1. Checkpoint: Partition a line segment 2. Checkpoint: Coordinate proofs 3. Checkpoint: Parallel and perpendicular lines
Checkpoint opportunity
1. Checkpoint: Partition a line segment 2. Checkpoint: Coordinate proofs 3. Checkpoint: Parallel and perpendicular lines
3 The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity).
A describe and perform transformations of figures in a plane using coordinate notation;		Translations 1. Translations: graph the image 2. Translations: find the coordinates 3. Translations: write the rule Reflections 4. Reflections: graph the image 5. Reflections: find the coordinates Rotations 6. Rotations: graph the image 7. Rotations: find the coordinates Mixed transformations 8. Reflections and rotations: write the rule 9. Congruence transformations: mixed review
A describe and perform transformations of figures in a plane using coordinate notation;
Translations 1. Translations: graph the image 2. Translations: find the coordinates 3. Translations: write the rule Reflections 4. Reflections: graph the image 5. Reflections: find the coordinates Rotations 6. Rotations: graph the image 7. Rotations: find the coordinates Mixed transformations 8. Reflections and rotations: write the rule 9. Congruence transformations: mixed review

B determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane;		1. Sequences of congruence transformations: graph the image
B determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane;
1. Sequences of congruence transformations: graph the image

C identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane; and		1. Classify congruence transformations 2. Sequences of congruence transformations: choose the sequence 3. Sequences of congruence transformations: find the rules 4. Similar triangles and similarity transformations
C identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane; and
1. Classify congruence transformations 2. Sequences of congruence transformations: choose the sequence 3. Sequences of congruence transformations: find the rules 4. Similar triangles and similarity transformations

D identify and distinguish between reflectional and rotational symmetry in a plane figure.		1. Line symmetry 2. Rotational symmetry
D identify and distinguish between reflectional and rotational symmetry in a plane figure.
1. Line symmetry 2. Rotational symmetry

Checkpoint opportunity		1. Checkpoint: Transformations of geometric figures
Checkpoint opportunity
1. Checkpoint: Transformations of geometric figures

4-5	Logical argument and constructions
4 The student uses the process skills with deductive reasoning to understand geometric relationships.
A distinguish between undefined terms, definitions, postulates, conjectures, and theorems;		1. Lines, line segments, and rays
A distinguish between undefined terms, definitions, postulates, conjectures, and theorems;
1. Lines, line segments, and rays

B identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse;		Logical statements 1. Identify hypotheses and conclusions 2. Conditionals 3. Converses, inverses, and contrapositives 4. Biconditionals Truth tables and truth values 5. Truth tables 6. Truth values
B identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse;
Logical statements 1. Identify hypotheses and conclusions 2. Conditionals 3. Converses, inverses, and contrapositives 4. Biconditionals Truth tables and truth values 5. Truth tables 6. Truth values

C verify that a conjecture is false using a counterexample; and		1. Counterexamples
C verify that a conjecture is false using a counterexample; and
1. Counterexamples

D compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.
D compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.

5 The student uses constructions to validate conjectures about geometric figures.
A investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools;		1. Interior angles of polygons
A investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools;
1. Interior angles of polygons

B construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge;		Points, lines, and segments 1. Construct a congruent segment 2. Construct the midpoint or perpendicular bisector of a segment 3. Construct a perpendicular line 4. Construct parallel lines Angles 5. Construct an angle bisector 6. Construct a congruent angle Two-dimensional figures 7. Construct an equilateral triangle or regular hexagon 8. Construct a square 9. Construct the circumcenter or incenter of a triangle 10. Construct the centroid or orthocenter of a triangle
B construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge;
Points, lines, and segments 1. Construct a congruent segment 2. Construct the midpoint or perpendicular bisector of a segment 3. Construct a perpendicular line 4. Construct parallel lines Angles 5. Construct an angle bisector 6. Construct a congruent angle Two-dimensional figures 7. Construct an equilateral triangle or regular hexagon 8. Construct a square 9. Construct the circumcenter or incenter of a triangle 10. Construct the centroid or orthocenter of a triangle

C use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships; and		1. Congruent line segments 2. Perpendicular Bisector Theorem 3. Angle bisectors
C use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships; and
1. Congruent line segments 2. Perpendicular Bisector Theorem 3. Angle bisectors

D verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.		1. Triangle Inequality Theorem
D verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.
1. Triangle Inequality Theorem

Checkpoint opportunity		1. Checkpoint: Geometric constructions
Checkpoint opportunity
1. Checkpoint: Geometric constructions

6	Proof and congruence
6 The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.
A verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems;		1. Perpendicular Bisector Theorem 2. Find measures of complementary, supplementary, vertical, and adjacent angles 3. Angle diagrams: solve for the variable 4. Proofs involving angles 5. Transversals of parallel lines: find angle measures 6. Transversals of parallel lines: solve for x 7. Proofs involving parallel lines I 8. Proofs involving parallel lines II
A verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems;
1. Perpendicular Bisector Theorem 2. Find measures of complementary, supplementary, vertical, and adjacent angles 3. Angle diagrams: solve for the variable 4. Proofs involving angles 5. Transversals of parallel lines: find angle measures 6. Transversals of parallel lines: solve for x 7. Proofs involving parallel lines I 8. Proofs involving parallel lines II

B prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions;		SSS and SAS Theorems 1. SSS and SAS Theorems 2. Proving triangles congruent by SSS and SAS 3. SSS Theorem in the coordinate plane ASA and AAS Theorems 4. ASA and AAS Theorems 5. Proving triangles congruent by ASA and AAS Hypotenuse-Leg Theorem 6. Hypotenuse-Leg Theorem Mixed congruence theorems 7. SSS, SAS, ASA, and AAS Theorems 8. Proving triangles congruent by SSS, SAS, ASA, and AAS
B prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions;
SSS and SAS Theorems 1. SSS and SAS Theorems 2. Proving triangles congruent by SSS and SAS 3. SSS Theorem in the coordinate plane ASA and AAS Theorems 4. ASA and AAS Theorems 5. Proving triangles congruent by ASA and AAS Hypotenuse-Leg Theorem 6. Hypotenuse-Leg Theorem Mixed congruence theorems 7. SSS, SAS, ASA, and AAS Theorems 8. Proving triangles congruent by SSS, SAS, ASA, and AAS

C apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles;		1. Congruence statements and corresponding parts 2. Identify congruent figures 3. Determine if two figures are congruent: justify your answer 4. Prove triangles are congruent using rigid motions 5. Proofs involving corresponding parts of congruent triangles
C apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles;
1. Congruence statements and corresponding parts 2. Identify congruent figures 3. Determine if two figures are congruent: justify your answer 4. Prove triangles are congruent using rigid motions 5. Proofs involving corresponding parts of congruent triangles

D verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems; and		Relationships in triangles 1. Triangle Angle-Sum Theorem 2. Congruency in isosceles and equilateral triangles 3. Proofs involving isosceles triangles 4. Midsegments of triangles 5. Identify medians, altitudes, angle bisectors, and perpendicular bisectors 6. Find the centroid of a triangle 7. Proofs involving triangles I Pythagorean theorem 8. Pythagorean theorem 9. Prove the Pythagorean theorem 10. Converse of the Pythagorean theorem
D verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems; and
Relationships in triangles 1. Triangle Angle-Sum Theorem 2. Congruency in isosceles and equilateral triangles 3. Proofs involving isosceles triangles 4. Midsegments of triangles 5. Identify medians, altitudes, angle bisectors, and perpendicular bisectors 6. Find the centroid of a triangle 7. Proofs involving triangles I Pythagorean theorem 8. Pythagorean theorem 9. Prove the Pythagorean theorem 10. Converse of the Pythagorean theorem

E prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems.		Classify quadrilaterals 1. Classify quadrilaterals I 2. Classify quadrilaterals II 3. Classify quadrilaterals on the coordinate plane: justify your answer Properties of quadrilaterals 4. Find missing angles in quadrilaterals 5. Properties of parallelograms 6. Properties of rhombuses 7. Properties of squares and rectangles Proofs 8. Proving a quadrilateral is a parallelogram
E prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems.
Classify quadrilaterals 1. Classify quadrilaterals I 2. Classify quadrilaterals II 3. Classify quadrilaterals on the coordinate plane: justify your answer Properties of quadrilaterals 4. Find missing angles in quadrilaterals 5. Properties of parallelograms 6. Properties of rhombuses 7. Properties of squares and rectangles Proofs 8. Proving a quadrilateral is a parallelogram

Checkpoint opportunity		1. Checkpoint: Line and angle theorems 2. Checkpoint: Parallelogram theorems 3. Checkpoint: Rigid motion and congruence 4. Checkpoint: Triangle theorems
Checkpoint opportunity
1. Checkpoint: Line and angle theorems 2. Checkpoint: Parallelogram theorems 3. Checkpoint: Rigid motion and congruence 4. Checkpoint: Triangle theorems

7-9	Similarity, proof, and trigonometry
7 The student uses the process skills in applying similarity to solve problems.
A apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles; and		Similar figures 1. Ratios in similar figures 2. Similarity statements 3. Identify similar figures 4. Side lengths and angle measures in similar figures 5. Similar triangles and similarity transformations 6. Determine if two figures are similar: justify your answer Similarity of circles 7. Similarity of circles Similar solids 8. Similar solids: find the missing length
A apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles; and
Similar figures 1. Ratios in similar figures 2. Similarity statements 3. Identify similar figures 4. Side lengths and angle measures in similar figures 5. Similar triangles and similarity transformations 6. Determine if two figures are similar: justify your answer Similarity of circles 7. Similarity of circles Similar solids 8. Similar solids: find the missing length

B apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems.		1. Similar triangles and indirect measurement 2. Angle-angle criterion for similar triangles
B apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems.
1. Similar triangles and indirect measurement 2. Angle-angle criterion for similar triangles

Checkpoint opportunity		1. Checkpoint: Similarity transformations
Checkpoint opportunity
1. Checkpoint: Similarity transformations
8 The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.
A prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems; and		1. Similarity rules for triangles 2. Triangle Proportionality Theorem 3. Prove similarity statements 4. Prove proportions or angle congruences using similarity 5. Proofs involving similarity in right triangles 6. Proofs involving triangles II
A prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems; and
1. Similarity rules for triangles 2. Triangle Proportionality Theorem 3. Prove similarity statements 4. Prove proportions or angle congruences using similarity 5. Proofs involving similarity in right triangles 6. Proofs involving triangles II

B identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.		1. Similarity and altitudes in right triangles 2. Proofs involving similarity in right triangles
B identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.
1. Similarity and altitudes in right triangles 2. Proofs involving similarity in right triangles

Checkpoint opportunity		1. Checkpoint: Triangle similarity and congruence
Checkpoint opportunity
1. Checkpoint: Triangle similarity and congruence
9 The student uses the process skills to understand and apply relationships in right triangles.
A determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems; and		1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios: find a side length 4. Trigonometric ratios: find an angle measure
A determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems; and
1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios: find a side length 4. Trigonometric ratios: find an angle measure

B apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems.		1. Pythagorean theorem 2. Special right triangles 3. Find trigonometric functions of special angles
B apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems.
1. Pythagorean theorem 2. Special right triangles 3. Find trigonometric functions of special angles

Checkpoint opportunity		1. Checkpoint: Right triangle trigonometry
Checkpoint opportunity
1. Checkpoint: Right triangle trigonometry

10-11	Two-dimensional and three-dimensional figures
10 The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures.
A identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes; and		1. Cross sections of three-dimensional figures 2. Solids of revolution
A identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes; and
1. Cross sections of three-dimensional figures 2. Solids of revolution

B determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change.		Perimeter and area 1. Perimeters of similar figures 2. Areas of similar figures 3. Area and perimeter of similar figures 4. Perimeter and area: changes in scale Surface area and volume 5. Surface area and volume of similar solids 6. Surface area and volume: changes in scale Perimeter, area, and volume 7. Perimeter, area, and volume: changes in scale
B determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change.
Perimeter and area 1. Perimeters of similar figures 2. Areas of similar figures 3. Area and perimeter of similar figures 4. Perimeter and area: changes in scale Surface area and volume 5. Surface area and volume of similar solids 6. Surface area and volume: changes in scale Perimeter, area, and volume 7. Perimeter, area, and volume: changes in scale

Checkpoint opportunity		1. Checkpoint: Cross sections and solids of revolution
Checkpoint opportunity
1. Checkpoint: Cross sections and solids of revolution
11 The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures.
A apply the formula for the area of regular polygons to solve problems using appropriate units of measure;		1. Area of regular polygons
A apply the formula for the area of regular polygons to solve problems using appropriate units of measure;
1. Area of regular polygons

B determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure;		1. Area of compound figures 2. Area between two shapes
B determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure;
1. Area of compound figures 2. Area between two shapes

C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure; and		1. Lateral area of prisms and cylinders 2. Lateral area of pyramids and cones 3. Surface area of prisms and cylinders 4. Surface area of pyramids and cones 5. Surface area of spheres
C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure; and
1. Lateral area of prisms and cylinders 2. Lateral area of pyramids and cones 3. Surface area of prisms and cylinders 4. Surface area of pyramids and cones 5. Surface area of spheres

D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.		1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres 4. Volume of compound figures
D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.
1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres 4. Volume of compound figures

Checkpoint opportunity		1. Checkpoint: Surface area 2. Checkpoint: Volume
Checkpoint opportunity
1. Checkpoint: Surface area 2. Checkpoint: Volume

12	Circles
12 The student uses the process skills to understand geometric relationships and apply theorems and equations about circles.
A apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems;		Arcs, chords, and tangents 1. Arcs and chords 2. Tangent lines 3. Perimeter of polygons with an inscribed circle 4. Inscribed angles Inscribed polygons 5. Angles in inscribed right triangles 6. Angles in inscribed quadrilaterals I 7. Angles in inscribed quadrilaterals II Angles and segments 8. Angles formed by chords, secants, and tangents 9. Segments formed by chords, secants, and tangents
A apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems;
Arcs, chords, and tangents 1. Arcs and chords 2. Tangent lines 3. Perimeter of polygons with an inscribed circle 4. Inscribed angles Inscribed polygons 5. Angles in inscribed right triangles 6. Angles in inscribed quadrilaterals I 7. Angles in inscribed quadrilaterals II Angles and segments 8. Angles formed by chords, secants, and tangents 9. Segments formed by chords, secants, and tangents

B apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems;		1. Understand arc length and sector area of a circle 2. Arc length
B apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems;
1. Understand arc length and sector area of a circle 2. Arc length

C apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems;		1. Understand arc length and sector area of a circle 2. Area of sectors
C apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems;
1. Understand arc length and sector area of a circle 2. Area of sectors

D describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle; and		1. Convert between radians and degrees 2. Radians and arc length
D describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle; and
1. Convert between radians and degrees 2. Radians and arc length

E show that the equation of a circle with center at the origin and radius r is x² + y² = r² and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)² + (y - k)² =r².		1. Derive equations of circles using the Pythagorean theorem 2. Write equations of circles in standard form from graphs
E show that the equation of a circle with center at the origin and radius r is x² + y² = r² and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)² + (y - k)² =r².
1. Derive equations of circles using the Pythagorean theorem 2. Write equations of circles in standard form from graphs

Checkpoint opportunity		1. Checkpoint: Angles and lines in circles 2. Checkpoint: Arc length and area of sectors 3. Checkpoint: Equations of circles
Checkpoint opportunity
1. Checkpoint: Angles and lines in circles 2. Checkpoint: Arc length and area of sectors 3. Checkpoint: Equations of circles

13	Probability
13 The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events.
A develop strategies to use permutations and combinations to solve contextual problems;		1. Permutations 2. Permutation and combination notation 3. Find probabilities using combinations and permutations
A develop strategies to use permutations and combinations to solve contextual problems;
1. Permutations 2. Permutation and combination notation 3. Find probabilities using combinations and permutations

B determine probabilities based on area to solve contextual problems;		1. Geometric probability
B determine probabilities based on area to solve contextual problems;
1. Geometric probability

C identify whether two events are independent and compute the probability of the two events occurring together with or without replacement;		1. Identify independent and dependent events 2. Probability of independent and dependent events 3. Identify independent events
C identify whether two events are independent and compute the probability of the two events occurring together with or without replacement;
1. Identify independent and dependent events 2. Probability of independent and dependent events 3. Identify independent events

D apply conditional probability in contextual problems; and		1. Find conditional probabilities 2. Find conditional probabilities using two-way frequency tables
D apply conditional probability in contextual problems; and
1. Find conditional probabilities 2. Find conditional probabilities using two-way frequency tables

E apply independence in contextual problems.		1. Identify independent events 2. Independence and conditional probability
E apply independence in contextual problems.
1. Identify independent events 2. Independence and conditional probability

Checkpoint opportunity		1. Checkpoint: Probability
Checkpoint opportunity
1. Checkpoint: Probability