MA.912.G: Geometry

MA.912.G.1: Understand geometric concepts, applications, and their representations with coordinate systems. Find lengths and midpoints of line segments, slopes, parallel and perpendicular lines, and equations of lines. Using a compass and straightedge, patty paper, a drawing program or other techniques, students also construct lines and angles, explaining and justifying the processes used.

MA.912.G.1.1: Find the lengths and midpoints of line segments in two-dimensional coordinate systems.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

MA.912.G.1.2: Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass or a drawing program, explaining and justifying the process used.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

MA.912.G.1.3: Identify and use the relationships between special pairs of angles formed by parallel lines and transversals.

Investigating Angle Theorems - Activity A

MA.912.G.1.4: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

Construct Parallel and Perpendicular Lines
Point-Slope Form of a Line - Activity A
Slope - Activity B

MA.912.G.2: Identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. Find measures of angles, sides, perimeters, and areas of polygons, justifying the methods used. Apply transformations to polygons. Relate geometry to algebra by using coordinate geometry to determine transformations. Use algebraic reasoning to determine congruence, similarity, and symmetry. Create and verify tessellations of the plane using polygons.

MA.912.G.2.2: Determine the measures of interior and exterior angles of polygons, justifying the method used.

Triangle Angle Sum - Activity A

MA.912.G.2.3: Use properties of congruent and similar polygons to solve mathematical or real-world problems.

Classifying Triangles
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

MA.912.G.2.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons.

Dilations
Holiday Snowflake Designer
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
Translations

MA.912.G.2.5: Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.).

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

MA.912.G.2.6: Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane.

Classifying Triangles
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

MA.912.G.2.7: Determine how changes in dimensions affect the perimeter and area of common geometric figures.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

MA.912.G.3: Classify and understand relationships among quadrilaterals (rectangle, parallelogram, kite, etc.). Relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas, and prove theorems involving quadrilaterals

MA.912.G.3.1: Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

MA.912.G.3.2: Compare and contrast special quadrilaterals on the basis of their properties.

Classifying Quadrilaterals - Activity B
Congruence in Right Triangles
Parallelogram Conditions
Special Quadrilaterals

MA.912.G.3.3: Use coordinate geometry to prove properties of congruent, regular and similar quadrilaterals.

Classifying Quadrilaterals - Activity B
Congruence in Right Triangles
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons
Special Quadrilaterals

MA.912.G.3.4: Prove theorems involving quadrilaterals.

Parallelogram Conditions

MA.912.G.4: Identify and describe various kinds of triangles (right, acute, scalene, isosceles, etc.). Define and construct altitudes, medians, and bisectors, and triangles congruent to given triangles. Prove that triangles are congruent or similar and use properties of these triangles to solve problems involving lengths and areas. Relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. Understand and apply the inequality theorems of triangles.

MA.912.G.4.1: Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

Classifying Triangles
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

MA.912.G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors, orthocenter, centroid, incenter, and circumcenter.

Concurrent Lines, Medians, and Altitudes

MA.912.G.4.3: Construct triangles congruent to given triangles.

Congruence in Right Triangles
Proving Triangles Congruent

MA.912.G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and areas.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

MA.912.G.4.5: Apply theorems involving segments divided proportionally.

Perimeters and Areas of Similar Figures
Polling: Neighborhood

MA.912.G.4.6: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

MA.912.G.4.7: Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem.

Triangle Inequalities

MA.912.G.4.8: Use coordinate geometry to prove properties of congruent, regular, and similar triangles.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

MA.912.G.5: Apply the Pythagorean Theorem to solving problems, including those involving the altitudes of right triangles and triangles with special angle relationships. Use special right triangles to solve problems using the properties of triangles.

MA.912.G.5.1: Prove and apply the Pythagorean Theorem and its converse.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

MA.912.G.5.2: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

Similarity in Right Triangles

MA.912.G.5.4: Solve real-world problems involving right triangles.

Classifying Triangles

MA.912.G.6: Define and understand ideas related to circles (radius, tangent, chord, etc.). Perform constructions, and prove theorems related to circles. Find measures of arcs and angles related to them, as well as measures of circumference and area. Relate geometry to algebra by finding the equation of a circle in the coordinate plane.

MA.912.G.6.1: Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them. Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons.

Chords and Arcs

MA.912.G.6.2: Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

Chords and Arcs
Circle: Circumference and Area

MA.912.G.6.3: Prove theorems related to circles, including related angles, chords, tangents, and secants.

Chords and Arcs

MA.912.G.6.4: Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).

Chords and Arcs
Inscribing Angles

MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

Circles

MA.912.G.6.7: Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle.

Circles

MA.912.G.7: Describe and make regular and nonregular polyhedra (cube, pyramid, tetrahedron, octahedron, etc.). Explore relationships among the faces, edges, and vertices of polyhedra. Describe sets of points on spheres, using terms such as great circle. Describe symmetries of solids, and understand the properties of congruent and similar solids.

MA.912.G.7.1: Describe and make regular, non-regular, and oblique polyhedra and sketch the net for a given polyhedron and vice versa.

Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

MA.912.G.7.3: Identify, sketch, find areas and/or perimeters of cross sections of solid objects.

Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

MA.912.G.7.4: Identify chords, tangents, radii, and great circles of spheres.

Chords and Arcs

MA.912.G.7.5: Explain and use formulas for lateral area, surface area, and volume of solids.

Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

MA.912.G.7.6: Identify and use properties of congruent and similar solids.

Congruence in Right Triangles

MA.912.G.7.7: Determine how changes in dimensions affect the surface area and volume of common geometric solids.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

MA.912.G.8: In a general sense, mathematics is problem solving. In all mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results. At this level, apply these skills to making conjectures, using axioms and theorems, constructing logical arguments, and writing geometric proofs. Learn about inductive and deductive reasoning and how to use counterexamples to show that a general statement is false.

MA.912.G.8.5: Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs.

Biconditional Statement
Conditional Statement
Simplifying Trigonometric Expressions

MA.912.G.8.6: Perform basic constructions using straightedge and compass, and/or drawing programs describing and justifying the procedures used. Distinguish between sketching, constructing and drawing geometric figures.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles