IXL Skill Plan | Minnesota Academic Standards: Geometry

Minnesota Academic Standards: Geometry

Skills available for Minnesota Geometry standards

Standard

Geometry & Measurement

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9-11.9.3	Geometry & Measurement
9-11.9.3.1 Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations.
9-11.9.3.1.1 Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate.		Surface area 1. Lateral area of pyramids and cones 2. Surface area of pyramids and cones 3. Surface area of spheres Volume 4. Volume of pyramids and cones 5. Volume of spheres
9-11.9.3.1.1 Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate.
Surface area 1. Lateral area of pyramids and cones 2. Surface area of pyramids and cones 3. Surface area of spheres Volume 4. Volume of pyramids and cones 5. Volume of spheres

9-11.9.3.1.2 Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures.		Two-dimensional figures 1. Area of compound figures 2. Area between two shapes 3. Nets and drawings of three-dimensional figures Three-dimensional figures 4. Volume of compound figures
9-11.9.3.1.2 Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures.
Two-dimensional figures 1. Area of compound figures 2. Area between two shapes 3. Nets and drawings of three-dimensional figures Three-dimensional figures 4. Volume of compound figures

9-11.9.3.1.3 Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems.		Customary and metric units 1. Convert between customary and metric systems 2. Convert rates and measurements: customary units 3. Convert rates and measurements: metric units 4. Convert square and cubic units of length Word problems 5. Unit prices with unit conversions 6. Multi-step problems with unit conversions 7. Rate of travel: word problems 8. Weighted averages: word problems
9-11.9.3.1.3 Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems.
Customary and metric units 1. Convert between customary and metric systems 2. Convert rates and measurements: customary units 3. Convert rates and measurements: metric units 4. Convert square and cubic units of length Word problems 5. Unit prices with unit conversions 6. Multi-step problems with unit conversions 7. Rate of travel: word problems 8. Weighted averages: word problems

9-11.9.3.1.4 Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively.		Similar figures 1. Similar solids: find the missing length Perimeter, area, and volume of similar figures 2. Perimeters of similar figures 3. Areas of similar figures 4. Area and perimeter of similar figures 5. Surface area and volume of similar solids Changes in scale 6. Perimeter and area: changes in scale 7. Surface area and volume: changes in scale 8. Perimeter, area, and volume: changes in scale
9-11.9.3.1.4 Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively.
Similar figures 1. Similar solids: find the missing length Perimeter, area, and volume of similar figures 2. Perimeters of similar figures 3. Areas of similar figures 4. Area and perimeter of similar figures 5. Surface area and volume of similar solids Changes in scale 6. Perimeter and area: changes in scale 7. Surface area and volume: changes in scale 8. Perimeter, area, and volume: changes in scale

9-11.9.3.1.5 Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements.		1. Precision 2. Greatest possible error 3. Minimum and maximum area and volume 4. Percent error 5. Percent error: area and volume
9-11.9.3.1.5 Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements.
1. Precision 2. Greatest possible error 3. Minimum and maximum area and volume 4. Percent error 5. Percent error: area and volume

Checkpoint opportunity		1. Checkpoint: Surface area 2. Checkpoint: Volume 3. Checkpoint: Units and quantities
Checkpoint opportunity
1. Checkpoint: Surface area 2. Checkpoint: Volume 3. Checkpoint: Units and quantities
9-11.9.3.2 Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.
9-11.9.3.2.1 Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.
9-11.9.3.2.1 Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.


9-11.9.3.2.2 Accurately interpret and use words and phrases such as "if…then," "if and only if," "all," and "not." Recognize the logical relationships between an "if…then" statement and its inverse, converse and contrapositive.		1. Identify hypotheses and conclusions 2. Conditionals 3. Negations 4. Converses, inverses, and contrapositives 5. Biconditionals
9-11.9.3.2.2 Accurately interpret and use words and phrases such as "if…then," "if and only if," "all," and "not." Recognize the logical relationships between an "if…then" statement and its inverse, converse and contrapositive.
1. Identify hypotheses and conclusions 2. Conditionals 3. Negations 4. Converses, inverses, and contrapositives 5. Biconditionals

9-11.9.3.2.3 Assess the validity of a logical argument and give counterexamples to disprove a statement.		1. Counterexamples
9-11.9.3.2.3 Assess the validity of a logical argument and give counterexamples to disprove a statement.
1. Counterexamples

9-11.9.3.2.4 Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations.		Angles 1. Proofs involving angles Parallel and perpendicular lines 2. Proofs involving parallel lines I 3. Proofs involving parallel lines II Congruent triangles 4. Proving triangles congruent by SSS and SAS 5. Proving triangles congruent by ASA and AAS 6. Proving triangles congruent by SSS, SAS, ASA, and AAS 7. Proofs involving corresponding parts of congruent triangles Triangle relationships 8. Proofs involving isosceles triangles 9. Proofs involving triangles I 10. Proofs involving triangles II 11. Prove the Pythagorean theorem Quadrilaterals 12. Proving a quadrilateral is a parallelogram 13. Proofs involving triangles and quadrilaterals 14. Proofs involving quadrilaterals Similarity 15. Prove similarity statements 16. Prove proportions or angle congruences using similarity 17. Proofs involving similarity in right triangles
9-11.9.3.2.4 Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations.
Angles 1. Proofs involving angles Parallel and perpendicular lines 2. Proofs involving parallel lines I 3. Proofs involving parallel lines II Congruent triangles 4. Proving triangles congruent by SSS and SAS 5. Proving triangles congruent by ASA and AAS 6. Proving triangles congruent by SSS, SAS, ASA, and AAS 7. Proofs involving corresponding parts of congruent triangles Triangle relationships 8. Proofs involving isosceles triangles 9. Proofs involving triangles I 10. Proofs involving triangles II 11. Prove the Pythagorean theorem Quadrilaterals 12. Proving a quadrilateral is a parallelogram 13. Proofs involving triangles and quadrilaterals 14. Proofs involving quadrilaterals Similarity 15. Prove similarity statements 16. Prove proportions or angle congruences using similarity 17. Proofs involving similarity in right triangles

9-11.9.3.2.5 Use technology tools to examine theorems, make and test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets.		Angles 1. Construct an angle bisector 2. Construct a congruent angle Points, lines, and segments 3. Construct a congruent segment 4. Construct the midpoint or perpendicular bisector of a segment 5. Construct a perpendicular line 6. Construct parallel lines Regular polygons 7. Construct an equilateral triangle or regular hexagon 8. Construct a square Triangles 9. Construct the circumcenter or incenter of a triangle 10. Construct the centroid or orthocenter of a triangle Circles 11. Construct a tangent line to a circle 12. Construct an equilateral triangle inscribed in a circle 13. Construct a square inscribed in a circle 14. Construct a regular hexagon inscribed in a circle 15. Construct the inscribed or circumscribed circle of a triangle
9-11.9.3.2.5 Use technology tools to examine theorems, make and test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets.
Angles 1. Construct an angle bisector 2. Construct a congruent angle Points, lines, and segments 3. Construct a congruent segment 4. Construct the midpoint or perpendicular bisector of a segment 5. Construct a perpendicular line 6. Construct parallel lines Regular polygons 7. Construct an equilateral triangle or regular hexagon 8. Construct a square Triangles 9. Construct the circumcenter or incenter of a triangle 10. Construct the centroid or orthocenter of a triangle Circles 11. Construct a tangent line to a circle 12. Construct an equilateral triangle inscribed in a circle 13. Construct a square inscribed in a circle 14. Construct a regular hexagon inscribed in a circle 15. Construct the inscribed or circumscribed circle of a triangle

Checkpoint opportunity		1. Checkpoint: Geometric constructions
Checkpoint opportunity
1. Checkpoint: Geometric constructions
9-11.9.3.3 Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
9-11.9.3.3.1 Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results.		Transversals of parallel lines 1. Transversals: name angle pairs 2. Transversals of parallel lines: find angle measures 3. Transversals of parallel lines: solve for x Proofs 4. Proofs involving parallel lines I 5. Proofs involving parallel lines II Lines on the coordinate plane 6. Slopes of parallel and perpendicular lines 7. Equations of parallel and perpendicular lines 8. Find the distance between two parallel lines Perpendicular bisectors 9. Perpendicular Bisector Theorem
9-11.9.3.3.1 Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results.
Transversals of parallel lines 1. Transversals: name angle pairs 2. Transversals of parallel lines: find angle measures 3. Transversals of parallel lines: solve for x Proofs 4. Proofs involving parallel lines I 5. Proofs involving parallel lines II Lines on the coordinate plane 6. Slopes of parallel and perpendicular lines 7. Equations of parallel and perpendicular lines 8. Find the distance between two parallel lines Perpendicular bisectors 9. Perpendicular Bisector Theorem

9-11.9.3.3.2 Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results.		Angles 1. Identify complementary, supplementary, vertical, adjacent, and congruent angles 2. Find measures of complementary, supplementary, vertical, and adjacent angles 3. Angle diagrams: solve for the variable 4. Angle bisectors 5. Proofs involving angles Triangles 6. Triangle Angle-Sum Theorem 7. Exterior Angle Theorem 8. Exterior Angle Inequality Polygons 9. Interior angles of polygons 10. Exterior angles of polygons 11. Review: interior and exterior angles of polygons
9-11.9.3.3.2 Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results.
Angles 1. Identify complementary, supplementary, vertical, adjacent, and congruent angles 2. Find measures of complementary, supplementary, vertical, and adjacent angles 3. Angle diagrams: solve for the variable 4. Angle bisectors 5. Proofs involving angles Triangles 6. Triangle Angle-Sum Theorem 7. Exterior Angle Theorem 8. Exterior Angle Inequality Polygons 9. Interior angles of polygons 10. Exterior angles of polygons 11. Review: interior and exterior angles of polygons

9-11.9.3.3.3 Know and apply properties of equilateral, isosceles and scalene triangles to solve problems and logically justify results.		Classify triangles 1. Classify triangles 2. Classify triangles on the coordinate plane: justify your answer Congruency and proofs 3. Congruency in isosceles and equilateral triangles 4. Proofs involving isosceles triangles 5. Proofs involving triangles I 6. Proofs involving triangles II Apply properties 7. Midsegments of triangles 8. Triangles and bisectors 9. Identify medians, altitudes, angle bisectors, and perpendicular bisectors 10. Angle-side relationships in triangles 11. Triangle Inequality Theorem
9-11.9.3.3.3 Know and apply properties of equilateral, isosceles and scalene triangles to solve problems and logically justify results.
Classify triangles 1. Classify triangles 2. Classify triangles on the coordinate plane: justify your answer Congruency and proofs 3. Congruency in isosceles and equilateral triangles 4. Proofs involving isosceles triangles 5. Proofs involving triangles I 6. Proofs involving triangles II Apply properties 7. Midsegments of triangles 8. Triangles and bisectors 9. Identify medians, altitudes, angle bisectors, and perpendicular bisectors 10. Angle-side relationships in triangles 11. Triangle Inequality Theorem

9-11.9.3.3.4 Apply the Pythagorean theorem and its converse to solve problems and logically justify results.		Pythagorean theorem 1. Pythagorean theorem 2. Prove the Pythagorean theorem 3. Pythagorean Inequality Theorems Converse of the Pythagorean theorem 4. Converse of the Pythagorean theorem
9-11.9.3.3.4 Apply the Pythagorean theorem and its converse to solve problems and logically justify results.
Pythagorean theorem 1. Pythagorean theorem 2. Prove the Pythagorean theorem 3. Pythagorean Inequality Theorems Converse of the Pythagorean theorem 4. Converse of the Pythagorean theorem

9-11.9.3.3.5 Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results.		1. Special right triangles
9-11.9.3.3.5 Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results.
1. Special right triangles

9-11.9.3.3.6 Know and apply properties of congruent and similar figures to solve problems and logically justify results.		Congruence 1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts 3. Identify congruent figures 4. Determine if two figures are congruent: justify your answer Congruent triangles 5. SSS and SAS Theorems 6. ASA and AAS Theorems 7. SSS, SAS, ASA, and AAS Theorems 8. SSS Theorem in the coordinate plane 9. Hypotenuse-Leg Theorem Proofs involving congruent triangles 10. Proving triangles congruent by SSS and SAS 11. Proving triangles congruent by ASA and AAS 12. Proving triangles congruent by SSS, SAS, ASA, and AAS 13. Proofs involving corresponding parts of congruent triangles Similarity 14. Ratios in similar figures 15. Similarity statements 16. Identify similar figures 17. Side lengths and angle measures in similar figures 18. Determine if two figures are similar: justify your answer Similar triangles 19. Similar triangles and indirect measurement 20. Angle-angle criterion for similar triangles 21. Similarity rules for triangles 22. Triangle Proportionality Theorem 23. Similarity and altitudes in right triangles Proofs involving similar triangles 24. Prove similarity statements 25. Prove proportions or angle congruences using similarity 26. Proofs involving similarity in right triangles
9-11.9.3.3.6 Know and apply properties of congruent and similar figures to solve problems and logically justify results.
Congruence 1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts 3. Identify congruent figures 4. Determine if two figures are congruent: justify your answer Congruent triangles 5. SSS and SAS Theorems 6. ASA and AAS Theorems 7. SSS, SAS, ASA, and AAS Theorems 8. SSS Theorem in the coordinate plane 9. Hypotenuse-Leg Theorem Proofs involving congruent triangles 10. Proving triangles congruent by SSS and SAS 11. Proving triangles congruent by ASA and AAS 12. Proving triangles congruent by SSS, SAS, ASA, and AAS 13. Proofs involving corresponding parts of congruent triangles Similarity 14. Ratios in similar figures 15. Similarity statements 16. Identify similar figures 17. Side lengths and angle measures in similar figures 18. Determine if two figures are similar: justify your answer Similar triangles 19. Similar triangles and indirect measurement 20. Angle-angle criterion for similar triangles 21. Similarity rules for triangles 22. Triangle Proportionality Theorem 23. Similarity and altitudes in right triangles Proofs involving similar triangles 24. Prove similarity statements 25. Prove proportions or angle congruences using similarity 26. Proofs involving similarity in right triangles

9-11.9.3.3.7 Use properties of polygons-including quadrilaterals and regular polygons-to define them, classify them, solve problems and logically justify results.		Classify polygons 1. Polygon vocabulary Classify quadrilaterals 2. Identify trapezoids 3. Classify quadrilaterals I 4. Classify quadrilaterals II Shapes on the coordinate plane 5. Graph quadrilaterals 6. Classify shapes on the coordinate plane: justify your answer Angles in quadrilaterals 7. Find missing angles in quadrilaterals 8. Angles in inscribed quadrilaterals I 9. Angles in inscribed quadrilaterals II Properties of quadrilaterals 10. Properties of parallelograms 11. Properties of rhombuses 12. Properties of squares and rectangles 13. Properties of trapezoids 14. Properties of kites 15. Review: properties of quadrilaterals Proofs 16. Proving a quadrilateral is a parallelogram 17. Proofs involving triangles and quadrilaterals 18. Proofs involving quadrilaterals
9-11.9.3.3.7 Use properties of polygons-including quadrilaterals and regular polygons-to define them, classify them, solve problems and logically justify results.
Classify polygons 1. Polygon vocabulary Classify quadrilaterals 2. Identify trapezoids 3. Classify quadrilaterals I 4. Classify quadrilaterals II Shapes on the coordinate plane 5. Graph quadrilaterals 6. Classify shapes on the coordinate plane: justify your answer Angles in quadrilaterals 7. Find missing angles in quadrilaterals 8. Angles in inscribed quadrilaterals I 9. Angles in inscribed quadrilaterals II Properties of quadrilaterals 10. Properties of parallelograms 11. Properties of rhombuses 12. Properties of squares and rectangles 13. Properties of trapezoids 14. Properties of kites 15. Review: properties of quadrilaterals Proofs 16. Proving a quadrilateral is a parallelogram 17. Proofs involving triangles and quadrilaterals 18. Proofs involving quadrilaterals

9-11.9.3.3.8 Know and apply properties of a circle to solve problems and logically justify results.		Circle properties 1. Central angles and arc measures 2. Understand arc length and sector area of a circle 3. Arc length 4. Area of sectors 5. Circle measurements: mixed review 6. Arcs and chords 7. Tangent lines 8. Perimeter of polygons with an inscribed circle Angles and segments 9. Angles formed by chords, secants, and tangents 10. Segments formed by chords, secants, and tangents Inscribed angles and polygons 11. Inscribed angles 12. Angles in inscribed right triangles 13. Angles in inscribed quadrilaterals I 14. Angles in inscribed quadrilaterals II
9-11.9.3.3.8 Know and apply properties of a circle to solve problems and logically justify results.
Circle properties 1. Central angles and arc measures 2. Understand arc length and sector area of a circle 3. Arc length 4. Area of sectors 5. Circle measurements: mixed review 6. Arcs and chords 7. Tangent lines 8. Perimeter of polygons with an inscribed circle Angles and segments 9. Angles formed by chords, secants, and tangents 10. Segments formed by chords, secants, and tangents Inscribed angles and polygons 11. Inscribed angles 12. Angles in inscribed right triangles 13. Angles in inscribed quadrilaterals I 14. Angles in inscribed quadrilaterals II

Checkpoint opportunity		1. Checkpoint: Triangle similarity and congruence 2. Checkpoint: Parallelogram theorems 3. Checkpoint: Line and angle theorems 4. Checkpoint: Triangle theorems 5. Checkpoint: Angles and lines in circles 6. Checkpoint: Arc length and area of sectors
Checkpoint opportunity
1. Checkpoint: Triangle similarity and congruence 2. Checkpoint: Parallelogram theorems 3. Checkpoint: Line and angle theorems 4. Checkpoint: Triangle theorems 5. Checkpoint: Angles and lines in circles 6. Checkpoint: Arc length and area of sectors
9-11.9.3.4 Solve real-world and mathematical geometric problems using algebraic methods.
9-11.9.3.4.1 Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.		1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios in similar right triangles
9-11.9.3.4.1 Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.
1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios in similar right triangles

9-11.9.3.4.2 Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios.		Trigonometric ratios 1. Find trigonometric functions of special angles 2. Find trigonometric functions using a calculator 3. Trigonometric ratios: find a side length Law of Sines and Law of Cosines 4. Law of Sines 5. Law of Cosines Solve a triangle 6. Solve a special right triangle 7. Solve a right triangle 8. Solve a triangle Area of a triangle 9. Area of a triangle: sine formula 10. Area of a triangle: Law of Sines
9-11.9.3.4.2 Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios.
Trigonometric ratios 1. Find trigonometric functions of special angles 2. Find trigonometric functions using a calculator 3. Trigonometric ratios: find a side length Law of Sines and Law of Cosines 4. Law of Sines 5. Law of Cosines Solve a triangle 6. Solve a special right triangle 7. Solve a right triangle 8. Solve a triangle Area of a triangle 9. Area of a triangle: sine formula 10. Area of a triangle: Law of Sines

9-11.9.3.4.3 Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.		1. Inverses of trigonometric functions 2. Trigonometric ratios: find an angle measure 3. Solve a right triangle 4. Dilations: find the scale factor and center of dilation
9-11.9.3.4.3 Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.
1. Inverses of trigonometric functions 2. Trigonometric ratios: find an angle measure 3. Solve a right triangle 4. Dilations: find the scale factor and center of dilation

9-11.9.3.4.4 Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.		Line segments 1. Midpoint formula: find the midpoint 2. Partition a line segment in a given ratio 3. Midpoint formula: find the endpoint Distance 4. Distance formula 5. Find the distance between a point and a line Area and perimeter 6. Area and perimeter in the coordinate plane I 7. Area and perimeter in the coordinate plane II Slope 8. Slopes of lines 9. Slopes of parallel and perpendicular lines Triangles 10. Find the centroid of a triangle Classify shapes 11. Classify shapes on the coordinate plane: justify your answer
9-11.9.3.4.4 Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.
Line segments 1. Midpoint formula: find the midpoint 2. Partition a line segment in a given ratio 3. Midpoint formula: find the endpoint Distance 4. Distance formula 5. Find the distance between a point and a line Area and perimeter 6. Area and perimeter in the coordinate plane I 7. Area and perimeter in the coordinate plane II Slope 8. Slopes of lines 9. Slopes of parallel and perpendicular lines Triangles 10. Find the centroid of a triangle Classify shapes 11. Classify shapes on the coordinate plane: justify your answer

9-11.9.3.4.5 Know the equation for the graph of a circle with radius r and center (h, k), (x - h)² + (y - k)² = r², and justify this equation using the Pythagorean theorem and properties of translations.		Parts of a circle 1. Find the center of a circle 2. Find the radius or diameter of a circle 3. Determine if a point lies on a circle Equations and graphs 4. Derive equations of circles using the Pythagorean theorem 5. Write equations of circles in standard form from graphs 6. Write equations of circles in standard form using properties 7. Graph circles from equations in standard form
9-11.9.3.4.5 Know the equation for the graph of a circle with radius r and center (h, k), (x - h)² + (y - k)² = r², and justify this equation using the Pythagorean theorem and properties of translations.
Parts of a circle 1. Find the center of a circle 2. Find the radius or diameter of a circle 3. Determine if a point lies on a circle Equations and graphs 4. Derive equations of circles using the Pythagorean theorem 5. Write equations of circles in standard form from graphs 6. Write equations of circles in standard form using properties 7. Graph circles from equations in standard form

9-11.9.3.4.6 Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid.		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. Rotate polygons about a point 7. Rotations: graph the image 8. Rotations: find the coordinates Dilations 9. Dilations: graph the image 10. Dilations: find the coordinates 11. Dilations: find length, perimeter, and area 12. Dilations: find the scale factor 13. Dilations: find the scale factor and center of the dilation 14. Dilations and parallel lines Congruence transformations 15. Classify congruence transformations 16. Reflections and rotations: write the rule 17. Transformations that carry a polygon onto itself 18. Congruence transformations: mixed review 19. Determine if two figures are congruent: justify your answer Sequences of congruence transformations 20. Glide reflections: graph the image 21. Sequences of congruence transformations: graph the image 22. Sequences of congruence transformations: choose the sequence 23. Sequences of congruence transformations: find the rules
9-11.9.3.4.6 Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid.
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. Rotate polygons about a point 7. Rotations: graph the image 8. Rotations: find the coordinates Dilations 9. Dilations: graph the image 10. Dilations: find the coordinates 11. Dilations: find length, perimeter, and area 12. Dilations: find the scale factor 13. Dilations: find the scale factor and center of the dilation 14. Dilations and parallel lines Congruence transformations 15. Classify congruence transformations 16. Reflections and rotations: write the rule 17. Transformations that carry a polygon onto itself 18. Congruence transformations: mixed review 19. Determine if two figures are congruent: justify your answer Sequences of congruence transformations 20. Glide reflections: graph the image 21. Sequences of congruence transformations: graph the image 22. Sequences of congruence transformations: choose the sequence 23. Sequences of congruence transformations: find the rules

9-11.9.3.4.7 Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean theorem to obtain a quadratic equation for a length in a geometric figure.		Segments and angles 1. Additive property of length 2. Perpendicular Bisector Theorem 3. Angle diagrams: solve for the variable 4. Angle bisectors 5. Transversals of parallel lines: solve for x Similarity 6. Side lengths and angle measures in similar figures 7. Similar triangles and indirect measurement 8. Triangle Proportionality Theorem 9. Similarity and altitudes in right triangles Pythagorean theorem 10. Pythagorean theorem
9-11.9.3.4.7 Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean theorem to obtain a quadratic equation for a length in a geometric figure.
Segments and angles 1. Additive property of length 2. Perpendicular Bisector Theorem 3. Angle diagrams: solve for the variable 4. Angle bisectors 5. Transversals of parallel lines: solve for x Similarity 6. Side lengths and angle measures in similar figures 7. Similar triangles and indirect measurement 8. Triangle Proportionality Theorem 9. Similarity and altitudes in right triangles Pythagorean theorem 10. Pythagorean theorem

Checkpoint opportunity		1. Checkpoint: Coordinate proofs 2. Checkpoint: Trigonometry 3. Checkpoint: Distance and midpoints in the coordinate plane 4. Checkpoint: Equations of circles 5. Checkpoint: Congruence transformations
Checkpoint opportunity
1. Checkpoint: Coordinate proofs 2. Checkpoint: Trigonometry 3. Checkpoint: Distance and midpoints in the coordinate plane 4. Checkpoint: Equations of circles 5. Checkpoint: Congruence transformations