Academic Standards

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.

Slope - Activity B

Distance Formula - Activity A

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.

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

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

Investigating Angle Theorems - Activity A

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

Triangle Angle Sum - Activity A

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.

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

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.

Reflections

Rotations, Reflections and Translations

Translations

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

Similar Figures - Activity A

Similar Polygons

Proving Triangles Congruent

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

Classifying Quadrilaterals - Activity B

Parallelogram Conditions

Special Quadrilaterals

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).

Classifying Quadrilaterals - Activity B

Classifying Triangles

Parallelogram Conditions

Simplifying Trigonometric Expressions

Special Quadrilaterals

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

Concurrent Lines, Medians, and Altitudes

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

Congruence in Right Triangles

Proving Triangles Congruent

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

Congruence in Right Triangles

Proving Triangles Congruent

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.

Classifying Triangles

Isosceles and Equilateral Triangles

Simplifying Trigonometric Expressions

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.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

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

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

Unit Circle

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.

Area of Parallelograms - Activity A

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.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

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

Chords and Arcs

Classifying Triangles

Parallelogram Conditions

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).

Chords and Arcs

Classifying Triangles

Inscribing Angles

Parallelogram Conditions

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

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

Simplifying Trigonometric Expressions

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.4.2: 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.

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

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.

Classifying Triangles

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

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.

Biconditional Statement

Conditional Statement

Simplifying Trigonometric Expressions

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.