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

Constructing Congruent Segments and Angles
Triangle Angle Sum

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

Point-Slope Form of a Line
Points, Lines, and Equations

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.2.1: Identify and describe convex, concave, regular, and irregular polygons.

Classifying Quadrilaterals
Special Parallelograms

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

Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

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
Reflections
Rotations, Reflections, and Translations
Similar Figures
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
Area of Triangles
Perimeter and Area of Rectangles

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

Dilations

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

Perimeter and Area of Rectangles

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.

Area of Parallelograms
Classifying Quadrilaterals
Parallelogram Conditions
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures
Similar Figures
Special Parallelograms

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

Classifying Quadrilaterals
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Similar Figures
Special Parallelograms

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

Parallelogram Conditions
Special Parallelograms

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

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
Similarity in Right Triangles

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

Perimeters and Areas of Similar Figures
Similar Figures

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
Proving Triangles Congruent
Similar Figures

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

Triangle Inequalities

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.

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

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.5.3: Use special right triangles (30° - 60°- 90° and 45° - 45°- 90°) to solve problems.

Cosine Function
Sine Function
Tangent Function

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

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

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
Circles
Concurrent Lines, Medians, and Altitudes
Inscribed Angles

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

Chords and Arcs
Circles
Circumference and Area of Circles
Inscribed Angles

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

Chords and Arcs
Inscribed Angles

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
Inscribed Angles

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

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

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

Surface and Lateral Areas of Prisms and Cylinders

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.8.2: Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

Estimating Population Size
Solving Equations on the Number Line