G.1: Students find lengths and midpoints of line segments. They describe and use parallel and perpendicular lines. They find slopes and equations of lines.

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

Distance Formula

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

Constructing Congruent Segments and Angles
Triangle Angle Sum

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

G.2: Students identify and describe polygons and measure interior and exterior angles. They use congruence, similarity, symmetry, tessellations, and transformations. They find measures of sides, perimeters, and areas.

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

Polygon Angle Sum

G.2.3: Use properties of congruent and similar polygons to solve problems.

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

G.2.5: Find and use measures of sides, perimeters, and areas of polygons, and relate these measures to each other using formulas.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures

G.3: Students identify and describe simple quadrilaterals. They use congruence and similarity. They find measures of sides, perimeters, and areas.

G.3.1: Describe, classify, and understand relationships among the quadrilaterals square, rectangle, rhombus, parallelogram, trapezoid, and kite.

Classifying Quadrilaterals

G.3.2: Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.

Perimeters and Areas of Similar Figures
Similar Figures

G.3.3: Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures to each other using formulas.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

G.4: Students identify and describe types of triangles. They identify and draw altitudes, medians, and angle bisectors. They use congruence and similarity. They find measures of sides, perimeters, and areas. They apply inequality theorems.

G.4.1: Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similarity in Right Triangles
Triangle Inequalities

G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.

Concurrent Lines, Medians, and Altitudes
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

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

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

Beam to Moon (Ratios and Proportions)
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

G.4.7: Find and use measures of sides, perimeters, and areas of triangles, and relate these measures to each other using formulas.

Area of Triangles

G.4.8: Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and hinge theorem.

Triangle Inequalities

G.5: Students prove the Pythagorean Theorem and use it to solve problems. They define and apply the trigonometric relations sine, cosine, and tangent.

G.5.1: Prove and use the Pythagorean Theorem.

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

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

Cosine Function
Sine Function
Tangent Function

G.5.4: Define and use the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) in terms of angles of right triangles.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

G.5.5: Know and use the relationship sin²x + cos²x = 1.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

G.6: Students define ideas related to circles: e.g., radius, tangent. They find measures of angles, lengths, and areas. They prove theorems about circles. They find equations of circles.

G.6.2: Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and tangent.

Chords and Arcs
Inscribed Angles

G.6.3: Prove theorems related to circles.

Inscribed Angles

G.6.4: Construct tangents to circles, and circumscribe and inscribe circles.

Circumference and Area of Circles
Concurrent Lines, Medians, and Altitudes
Inscribed Angles

G.6.7: Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use these measures to solve problems.

Circumference and Area of Circles
Inscribed Angles

G.7: Students describe and make polyhedra and other solids. They describe relationships and symmetries, and use congruence and similarity.

G.7.7: Find and use measures of sides, volumes of solids, and surface areas of solids, and relate these measures to each other using formulas.

Pyramids and Cones

G.8: Mathematical Reasoning and Problem Solving

G.8.1: 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.

Linear Inequalities in Two Variables
Modeling One-Step Equations
Solving Equations on the Number Line
Using Algebraic Equations

G.8.6: Identify and give examples of undefined terms, axioms, and theorems, and inductive and deductive proof.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Parallel, Intersecting, and Skew Lines

G.8.7: Construct logical arguments, judge their validity, and give counterexamples to disprove statements.

Biconditional Statements
Conditional Statements