#### G.1: Points, Lines, Angles and Planes

G.1.1: Find the length of line segments in one- or two-dimensional coordinate systems, the slopes of line segments in two-dimensional coordinate systems, and find the point that is a given fractional distance from one end of the segment to another.

G.1.2: Construct congruent segments and angles, angle bisectors, perpendicular bisectors, and parallel and perpendicular lines by using appropriate geometric construction tools. Explain and justify the process used.

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

#### G.2: Polygons

G.2.1: Justifying the method used, find and use the sum of the measures of interior and exterior angles of convex polygons.

G.2.2: Identify types of symmetry (i.e., line, point, rotational, self-congruences) of polygons.

G.2.3: Solve problems involving congruent and similar polygons.

G.2.4: Predict and describe the results of translations, reflections and rotations on polygons. Describe a motion or series of motions that will show that two shapes are congruent.

G.2.7: Develop simple geometric proofs involving congruent and similar polygons and provide reasons for each statement.

G.2.8: Describe, classify and recognize relationships among the quadrilaterals, such as squares, rectangles, rhombuses, parallelograms, trapezoids and kites.

G.2.9: Prove and apply theorems about parallelograms and trapezoids (including isosceles trapezoids) involving their angles, sides and diagonals. Prove that the given quadrilaterals are parallelograms, rhombuses, rectangles, squares or trapezoids (as appropriate).

G.2.10: Define, identify, construct and solve problems involving perpendicular bisectors, angle bisectors, medians and altitudes in triangles.

G.2.11: Construct triangles congruent to given triangles. Explain and justify the process used.

G.2.12: Use theorems to show if two triangles are congruent (i.e., SSS, SAS, ASA) or similar (i.e., AA, SAS, SSS).

G.2.13: Prove and apply the triangle inequality theorem.

G.2.14: Develop simple geometric proofs involving triangles and provide reasons for each statement of the proof.

G.2.15: Prove and apply the isosceles triangle theorem and its converse.

G.2.16: Prove the Pythagorean Theorem and its converse and use them to solve problems, including problems involving the length of a segment in the coordinate plane.

G.2.19: Define and use the trigonometric functions sine, cosine and tangent in terms of angles of right triangles.

G.2.20: Deduce and apply the area formula A= 1/2 absinC, where a and b are the lengths of two sides of a triangle and C is the measure of the included angle formed by the two sides.

G.2.21: Solve problems that can be modeled using right triangles, including problems that can be modeled using trigonometric functions. Interpret the solutions and determine whether the solutions are reasonable. Use technology as appropriate.

#### G.3: Circles

G.3.2: Define, deduce and use formulas for, and prove theorems for radius, diameter, chord, secant and tangent.

G.3.3: Define, deduce and use formulas for, and prove theorems for measures of arcs and related angles (i.e., central, inscribed and intersections of secants and tangents).

G.3.4: Define, deduce and use formulas for, and prove theorems for measures of circumference, arc length, and areas of circles and sectors.

G.3.5: Find the equation of a circle in the coordinate plane in terms of its center and radius and determine how the graph of a circle changes if a, b and r change in the equation (x - a)² + (y - b)² = r².

#### G.4: Polyhedra and Other Solids

G.4.2: Solve problems involving congruent and similar solids.

G.4.3: Find and use measures of sides, volumes and surface areas of prisms, regular pyramids, cylinders, right circular cones and spheres. Relate these measures to each other using formulas.

G.4.4: Visualize solids and surfaces in three-dimensional space when given two-dimensional representations, and create two-dimensional representations for the surfaces of three-dimensional objects.

#### G.5: Geometric Reasoning and Proof

G.5.3: Understand the differences among supporting evidence, counterexamples and actual proofs.

G.5.4: Develop simple geometric proofs (i.e., direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry) using two-column, paragraphs and flow charts formats. Provide reasons for each statement in the proofs.

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.