#### 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.

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

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

#### 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.

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

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

#### 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.

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

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

#### 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.

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

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

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

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

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

#### 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.

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

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

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

#### 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.

G.6.3: Prove theorems related to circles.

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

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

#### 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.

#### 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.

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

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

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.