IXL Skill Plan | Florida's B.E.S.T. Standards: Geometry

Florida's B.E.S.T. Standards: Geometry

Skills available for Florida Geometry standards

Strand

Geometric Reasoning
Trigonometry
Logic and Discrete Theory

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GR	Geometric Reasoning
MA.912.GR.1 Prove and apply geometric theorems to solve problems.
MA.912.GR.1.1 Prove relationships and theorems about lines and angles. Solve mathematical and real-world problems involving postulates, relationships and theorems of lines and angles.		1. Proofs involving angles 2. Transversals of parallel lines: find angle measures 3. Transversals of parallel lines: solve for x 4. Proofs involving parallel lines I 5. Proofs involving parallel lines II
MA.912.GR.1.1 Prove relationships and theorems about lines and angles. Solve mathematical and real-world problems involving postulates, relationships and theorems of lines and angles.
1. Proofs involving angles 2. Transversals of parallel lines: find angle measures 3. Transversals of parallel lines: solve for x 4. Proofs involving parallel lines I 5. Proofs involving parallel lines II

MA.912.GR.1.2 Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.		Congruence theorems 1. SSS and SAS Theorems 2. ASA and AAS Theorems 3. SSS, SAS, ASA, and AAS Theorems 4. SSS Theorem in the coordinate plane Prove triangle 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 Similarity theorems 8. Similarity rules for triangles Prove triangle similarity 9. Prove similarity statements
MA.912.GR.1.2 Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
Congruence theorems 1. SSS and SAS Theorems 2. ASA and AAS Theorems 3. SSS, SAS, ASA, and AAS Theorems 4. SSS Theorem in the coordinate plane Prove triangle 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 Similarity theorems 8. Similarity rules for triangles Prove triangle similarity 9. Prove similarity statements

MA.912.GR.1.3 Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.		Angle relationships 1. Triangle Angle-Sum Theorem 2. Exterior Angle Theorem 3. Exterior Angle Inequality 4. Proofs involving triangles I Segment relationships 5. Midsegments of triangles 6. Triangle Inequality Theorem 7. Proofs involving triangles II Isosceles, equilateral, and right triangles 8. Congruency in isosceles and equilateral triangles 9. Proofs involving isosceles triangles 10. Hypotenuse-Leg Theorem
MA.912.GR.1.3 Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.
Angle relationships 1. Triangle Angle-Sum Theorem 2. Exterior Angle Theorem 3. Exterior Angle Inequality 4. Proofs involving triangles I Segment relationships 5. Midsegments of triangles 6. Triangle Inequality Theorem 7. Proofs involving triangles II Isosceles, equilateral, and right triangles 8. Congruency in isosceles and equilateral triangles 9. Proofs involving isosceles triangles 10. Hypotenuse-Leg Theorem

MA.912.GR.1.4 Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.		1. Properties of parallelograms 2. Proving a quadrilateral is a parallelogram 3. Properties of squares and rectangles 4. Proofs involving triangles and quadrilaterals 5. Proofs involving quadrilaterals
MA.912.GR.1.4 Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.
1. Properties of parallelograms 2. Proving a quadrilateral is a parallelogram 3. Properties of squares and rectangles 4. Proofs involving triangles and quadrilaterals 5. Proofs involving quadrilaterals

MA.912.GR.1.5 Prove relationships and theorems about trapezoids. Solve mathematical and real-world problems involving postulates, relationships and theorems of trapezoids.		1. Proofs involving triangles and quadrilaterals 2. Proofs involving quadrilaterals 3. Properties of trapezoids
MA.912.GR.1.5 Prove relationships and theorems about trapezoids. Solve mathematical and real-world problems involving postulates, relationships and theorems of trapezoids.
1. Proofs involving triangles and quadrilaterals 2. Proofs involving quadrilaterals 3. Properties of trapezoids

MA.912.GR.1.6 Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.		Congruent figures 1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts 3. Identify congruent figures Similar figures 4. Ratios in similar figures 5. Similarity statements 6. Identify similar figures 7. Side lengths and angle measures in similar figures 8. Perimeters of similar figures 9. Areas of similar figures Similar triangles 10. Similar triangles and indirect measurement 11. Similarity and altitudes in right triangles 12. Prove proportions or angle congruences using similarity 13. Proofs involving similarity in right triangles
MA.912.GR.1.6 Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.
Congruent figures 1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts 3. Identify congruent figures Similar figures 4. Ratios in similar figures 5. Similarity statements 6. Identify similar figures 7. Side lengths and angle measures in similar figures 8. Perimeters of similar figures 9. Areas of similar figures Similar triangles 10. Similar triangles and indirect measurement 11. Similarity and altitudes in right triangles 12. Prove proportions or angle congruences using similarity 13. Proofs involving similarity in right triangles

Checkpoint opportunity		1. Checkpoint: Line and angle theorems 2. Checkpoint: Triangle similarity and congruence 3. Checkpoint: Parallelogram theorems 4. Checkpoint: Triangle theorems
Checkpoint opportunity
1. Checkpoint: Line and angle theorems 2. Checkpoint: Triangle similarity and congruence 3. Checkpoint: Parallelogram theorems 4. Checkpoint: Triangle theorems
MA.912.GR.2 Apply properties of transformations to describe congruence or similarity.
MA.912.GR.2.1 Given a preimage and image, describe the transformation and represent the transformation algebraically using coordinates.		Translations 1. Translations: find the coordinates 2. Translations: write the rule Reflections 3. Reflections: find the coordinates Rotations 4. Rotations: find the coordinates Congruence transformations 5. Classify congruence transformations 6. Reflections and rotations: write the rule 7. Congruence transformations: mixed review Dilations 8. Dilations: find the coordinates 9. Dilations: find the scale factor
MA.912.GR.2.1 Given a preimage and image, describe the transformation and represent the transformation algebraically using coordinates.
Translations 1. Translations: find the coordinates 2. Translations: write the rule Reflections 3. Reflections: find the coordinates Rotations 4. Rotations: find the coordinates Congruence transformations 5. Classify congruence transformations 6. Reflections and rotations: write the rule 7. Congruence transformations: mixed review Dilations 8. Dilations: find the coordinates 9. Dilations: find the scale factor

MA.912.GR.2.2 Identify transformations that do or do not preserve distance.
MA.912.GR.2.2 Identify transformations that do or do not preserve distance.


MA.912.GR.2.3 Identify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.		1. Sequences of congruence transformations: choose the sequence 2. Sequences of congruence transformations: find the rules 3. Transformations that carry a polygon onto itself
MA.912.GR.2.3 Identify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.
1. Sequences of congruence transformations: choose the sequence 2. Sequences of congruence transformations: find the rules 3. Transformations that carry a polygon onto itself

MA.912.GR.2.5 Given a geometric figure and a sequence of transformations, draw the transformed figure on a coordinate plane.		Single transformations 1. Translations: graph the image 2. Reflections: graph the image 3. Rotations: graph the image 4. Dilations: graph the image Sequence of transformations 5. Sequences of congruence transformations: graph the image
MA.912.GR.2.5 Given a geometric figure and a sequence of transformations, draw the transformed figure on a coordinate plane.
Single transformations 1. Translations: graph the image 2. Reflections: graph the image 3. Rotations: graph the image 4. Dilations: graph the image Sequence of transformations 5. Sequences of congruence transformations: graph the image

MA.912.GR.2.6 Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.		1. Determine if two figures are congruent: justify your answer 2. Prove triangles are congruent using rigid motions
MA.912.GR.2.6 Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.
1. Determine if two figures are congruent: justify your answer 2. Prove triangles are congruent using rigid motions

MA.912.GR.2.8 Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.		1. Similar triangles and similarity transformations 2. Determine if two figures are similar: justify your answer
MA.912.GR.2.8 Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.
1. Similar triangles and similarity transformations 2. Determine if two figures are similar: justify your answer

Checkpoint opportunity		1. Checkpoint: Congruence transformations 2. Checkpoint: Rigid motion and congruence 3. Checkpoint: Similarity transformations
Checkpoint opportunity
1. Checkpoint: Congruence transformations 2. Checkpoint: Rigid motion and congruence 3. Checkpoint: Similarity transformations
MA.912.GR.3 Use coordinate geometry to solve problems or prove relationships.
MA.912.GR.3.1 Determine the weighted average of two or more points on a line.		1. Weighted averages
MA.912.GR.3.1 Determine the weighted average of two or more points on a line.
1. Weighted averages

MA.912.GR.3.2 Given a mathematical or real-world context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.		1. SSS Theorem in the coordinate plane 2. Classify shapes on the coordinate plane: justify your answer
MA.912.GR.3.2 Given a mathematical or real-world context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.
1. SSS Theorem in the coordinate plane 2. Classify shapes on the coordinate plane: justify your answer

MA.912.GR.3.3 Use coordinate geometry to solve mathematical and real-world geometric problems involving lines, circles, triangles and quadrilaterals.		Parallel and perpendicular lines 1. Slopes of parallel and perpendicular lines 2. Equations of parallel and perpendicular lines 3. Find the distance between two parallel lines Partition line segments 4. Midpoint formula: find the midpoint 5. Partition a line segment in a given ratio 6. Midpoint formula: find the endpoint Circles 7. Find the radius or diameter of a circle 8. Determine if a point lies on a circle Triangles 9. Find the centroid of a triangle
MA.912.GR.3.3 Use coordinate geometry to solve mathematical and real-world geometric problems involving lines, circles, triangles and quadrilaterals.
Parallel and perpendicular lines 1. Slopes of parallel and perpendicular lines 2. Equations of parallel and perpendicular lines 3. Find the distance between two parallel lines Partition line segments 4. Midpoint formula: find the midpoint 5. Partition a line segment in a given ratio 6. Midpoint formula: find the endpoint Circles 7. Find the radius or diameter of a circle 8. Determine if a point lies on a circle Triangles 9. Find the centroid of a triangle

MA.912.GR.3.4 Use coordinate geometry to solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.		1. Area and perimeter in the coordinate plane I 2. Area and perimeter in the coordinate plane II
MA.912.GR.3.4 Use coordinate geometry to solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.
1. Area and perimeter in the coordinate plane I 2. Area and perimeter in the coordinate plane II

Checkpoint opportunity		1. Checkpoint: Partition a line segment 2. Checkpoint: Coordinate proofs 3. Checkpoint: Area and perimeter in the coordinate plane
Checkpoint opportunity
1. Checkpoint: Partition a line segment 2. Checkpoint: Coordinate proofs 3. Checkpoint: Area and perimeter in the coordinate plane
MA.912.GR.4 Use geometric measurement and dimensions to solve problems.
MA.912.GR.4.1 Identify the shapes of two-dimensional cross-sections of three-dimensional figures.		1. Cross sections of three-dimensional figures
MA.912.GR.4.1 Identify the shapes of two-dimensional cross-sections of three-dimensional figures.
1. Cross sections of three-dimensional figures

MA.912.GR.4.2 Identify three-dimensional objects generated by rotations of two-dimensional figures.		1. Solids of revolution
MA.912.GR.4.2 Identify three-dimensional objects generated by rotations of two-dimensional figures.
1. Solids of revolution

MA.912.GR.4.3 Extend previous understanding of scale drawings and scale factors to determine how dilations affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.		1. Perimeter and area: changes in scale 2. Surface area and volume: changes in scale 3. Perimeter, area, and volume: changes in scale
MA.912.GR.4.3 Extend previous understanding of scale drawings and scale factors to determine how dilations affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.
1. Perimeter and area: changes in scale 2. Surface area and volume: changes in scale 3. Perimeter, area, and volume: changes in scale

MA.912.GR.4.4 Solve mathematical and real-world problems involving the area of two-dimensional figures.		Polygons 1. Area of rectangles and squares 2. Area of parallelograms and triangles 3. Area of trapezoids 4. Area of regular polygons Circles 5. Area and circumference of circles Complex figures 6. Area of compound figures 7. Area between two shapes
MA.912.GR.4.4 Solve mathematical and real-world problems involving the area of two-dimensional figures.
Polygons 1. Area of rectangles and squares 2. Area of parallelograms and triangles 3. Area of trapezoids 4. Area of regular polygons Circles 5. Area and circumference of circles Complex figures 6. Area of compound figures 7. Area between two shapes

MA.912.GR.4.5 Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.		Volume 1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres Surface area and volume 4. Similar solids: find the missing length 5. Surface area and volume of similar solids 6. Surface area and volume review
MA.912.GR.4.5 Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
Volume 1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres Surface area and volume 4. Similar solids: find the missing length 5. Surface area and volume of similar solids 6. Surface area and volume review

MA.912.GR.4.6 Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.		Surface area 1. Surface area of prisms and cylinders 2. Surface area of pyramids and cones 3. Surface area of spheres Surface area and volume 4. Similar solids: find the missing length 5. Surface area and volume of similar solids 6. Surface area and volume review
MA.912.GR.4.6 Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
Surface area 1. Surface area of prisms and cylinders 2. Surface area of pyramids and cones 3. Surface area of spheres Surface area and volume 4. Similar solids: find the missing length 5. Surface area and volume of similar solids 6. Surface area and volume review

Checkpoint opportunity		1. Checkpoint: Surface area 2. Checkpoint: Density 3. Checkpoint: Cross sections and solids of revolution 4. Checkpoint: Volume
Checkpoint opportunity
1. Checkpoint: Surface area 2. Checkpoint: Density 3. Checkpoint: Cross sections and solids of revolution 4. Checkpoint: Volume
MA.912.GR.5 Make formal geometric constructions with a variety of tools and methods.
MA.912.GR.5.1 Construct a copy of a segment or an angle.		1. Construct a congruent segment 2. Construct a congruent angle
MA.912.GR.5.1 Construct a copy of a segment or an angle.
1. Construct a congruent segment 2. Construct a congruent angle

MA.912.GR.5.2 Construct the bisector of a segment or an angle, including the perpendicular bisector of a line segment.		1. Construct the midpoint or perpendicular bisector of a segment 2. Construct an angle bisector
MA.912.GR.5.2 Construct the bisector of a segment or an angle, including the perpendicular bisector of a line segment.
1. Construct the midpoint or perpendicular bisector of a segment 2. Construct an angle bisector

MA.912.GR.5.3 Construct the inscribed and circumscribed circles of a triangle.		1. Construct the circumcenter or incenter of a triangle 2. Construct the inscribed or circumscribed circle of a triangle
MA.912.GR.5.3 Construct the inscribed and circumscribed circles of a triangle.
1. Construct the circumcenter or incenter of a triangle 2. Construct the inscribed or circumscribed circle of a triangle

Checkpoint opportunity		1. Checkpoint: Geometric constructions
Checkpoint opportunity
1. Checkpoint: Geometric constructions
MA.912.GR.6 Use properties and theorems related to circles.
MA.912.GR.6.1 Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.		1. Arcs and chords 2. Tangent lines 3. Segments formed by chords, secants, and tangents
MA.912.GR.6.1 Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.
1. Arcs and chords 2. Tangent lines 3. Segments formed by chords, secants, and tangents

MA.912.GR.6.2 Solve mathematical and real-world problems involving the measures of arcs and related angles.		1. Central angles and arc measures 2. Arcs and chords 3. Inscribed angles 4. Angles formed by chords, secants, and tangents
MA.912.GR.6.2 Solve mathematical and real-world problems involving the measures of arcs and related angles.
1. Central angles and arc measures 2. Arcs and chords 3. Inscribed angles 4. Angles formed by chords, secants, and tangents

MA.912.GR.6.3 Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.		1. Angles in inscribed right triangles 2. Angles in inscribed quadrilaterals I 3. Angles in inscribed quadrilaterals II
MA.912.GR.6.3 Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.
1. Angles in inscribed right triangles 2. Angles in inscribed quadrilaterals I 3. Angles in inscribed quadrilaterals II

MA.912.GR.6.4 Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.		1. Understand arc length and sector area of a circle 2. Arc length 3. Area of sectors
MA.912.GR.6.4 Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.
1. Understand arc length and sector area of a circle 2. Arc length 3. Area of sectors

Checkpoint opportunity		1. Checkpoint: Angles and lines in circles 2. Checkpoint: Inscribed and circumscribed circles 3. Checkpoint: Arc length and area of sectors
Checkpoint opportunity
1. Checkpoint: Angles and lines in circles 2. Checkpoint: Inscribed and circumscribed circles 3. Checkpoint: Arc length and area of sectors
MA.912.GR.7 Apply geometric and algebraic representations of conic sections.
MA.912.GR.7.2 Given a mathematical or real-world context, derive and create the equation of a circle using key features.		1. Derive equations of circles using the Pythagorean theorem 2. Write equations of circles in standard form from graphs 3. Write equations of circles in standard form using properties 4. Convert equations of circles from general to standard form
MA.912.GR.7.2 Given a mathematical or real-world context, derive and create the equation of a circle using key features.
1. Derive equations of circles using the Pythagorean theorem 2. Write equations of circles in standard form from graphs 3. Write equations of circles in standard form using properties 4. Convert equations of circles from general to standard form

MA.912.GR.7.3 Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context.		1. Find properties of circles from equations in general form 2. Graph circles from equations in standard form 3. Graph circles from equations in general form
MA.912.GR.7.3 Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context.
1. Find properties of circles from equations in general form 2. Graph circles from equations in standard form 3. Graph circles from equations in general form

Checkpoint opportunity		1. Checkpoint: Equations of circles
Checkpoint opportunity
1. Checkpoint: Equations of circles

T	Trigonometry
MA.912.T.1 Define and use trigonometric ratios, identities or functions to solve problems.
MA.912.T.1.1 Define trigonometric ratios for acute angles in right triangles.		1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios: csc, sec, and cot 4. Trigonometric ratios in similar right triangles
MA.912.T.1.1 Define trigonometric ratios for acute angles in right triangles.
1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios: csc, sec, and cot 4. Trigonometric ratios in similar right triangles

MA.912.T.1.2 Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.		Pythagorean Theorem 1. Pythagorean theorem 2. Converse of the Pythagorean theorem 3. Pythagorean Inequality Theorems Trigonometric ratios 4. Trigonometric ratios: find a side length 5. Trigonometric ratios: find an angle measure Special right triangles 6. Special right triangles Solve a right triangle 7. Solve a right triangle
MA.912.T.1.2 Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.
Pythagorean Theorem 1. Pythagorean theorem 2. Converse of the Pythagorean theorem 3. Pythagorean Inequality Theorems Trigonometric ratios 4. Trigonometric ratios: find a side length 5. Trigonometric ratios: find an angle measure Special right triangles 6. Special right triangles Solve a right triangle 7. Solve a right triangle

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

LT	Logic and Discrete Theory
MA.912.LT.4 Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.
MA.912.LT.4.3 Identify and accurately interpret "if…then," "if and only if," "all" and "not" statements. Find the converse, inverse and contrapositive of a statement.		1. Identify hypotheses and conclusions 2. Converses, inverses, and contrapositives
MA.912.LT.4.3 Identify and accurately interpret "if…then," "if and only if," "all" and "not" statements. Find the converse, inverse and contrapositive of a statement.
1. Identify hypotheses and conclusions 2. Converses, inverses, and contrapositives

MA.912.LT.4.10 Judge the validity of arguments and give counterexamples to disprove statements.		1. Counterexamples
MA.912.LT.4.10 Judge the validity of arguments and give counterexamples to disprove statements.
1. Counterexamples