Gizmos for Arkansas - Mathematics: Geometry (Academic Standards adopted 2023)

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

G.RT: : Right Triangles

1.1: : Special Right Triangles & Pythagorean Theorem

1.1.1: : Students explore right triangles and apply the Pythagorean Theorem.

G.RT.1: : Apply the properties of special right triangles (30°- 60°- 90° and 45°- 45°- 90°) to solve real-world and mathematical problems.

G.RT.2: : Prove and apply the Pythagorean Theorem and its converse.

1.2: : Trigonometry Ratios

1.2.1: : Students apply trigonometric ratios to solve problems.

G.RT.3: : Explain how the definitions for trigonometric ratios are developed by similarity and how the side ratios in right triangles are properties of the angles in the triangle.

G.RT.4: : Explain the relationship between the sine and cosine of complementary angles and use them to solve problems.

G.RT.5: : Determine the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles.

G.RT.6: : Use trigonometric ratios (sine, cosine, and tangent) to calculate missing side lengths and angle measures in a right triangle, including applications of angles of elevation and depression; include real-world and mathematical problems.

G.CIR: : Circles

2.1: : Circle Relationships

2.1.1: : Students explore and use circle relationships to solve problems.

G.CIR.2: : Recognize and apply relationships between angles, radii, and chords, tangents, and secants including:

G.CIR.2.1: : The relationship between central, inscribed, and circumscribed angles,

G.CIR.2.2: : Inscribed angles on a diameter are right angles,

G.CIR.2.4: : The relationship of angles and segments formed by chords, secants and/or tangents to a circle.

2.2: : Equation of a Circle

2.2.1: : Students solve problems involving the equation of a circle.

G.CIR.6: : Write the equation of a circle, given the radius and center, where the center is at the origin or another point.

G.CIR.7: : Identify the center and radius of a circle, given the equation of a circle, where the center is at the origin or another point.

G.CIR.8: : Apply the equation of a circle to solve real-world problems.

G.GF: : Geometric Figures

3.1: : Three-Dimensional

3.1.1: : Students explore and solve problems involving three-dimensional figures.

G.GF.2: : Use three-dimensional geometric figures and their measures to model real-world objects and solve problems.

G.GF.3: : Explain why the formulas for the volume and surface area of a cylinder, pyramid, and cone work.

G.GF.4: : Apply the Pythagorean Theorem to determine missing measurements in a three-dimensional figure.

G.GF.5: : Identify the three-dimensional figure generated by rotating a two-dimensional figure.

3.2: : Two-Dimensional

3.2.1: : Students explore and solve problems involving two-dimensional figures.

G.GF.6: : Apply theorems about quadrilaterals, including those involving angles, diagonals, and sides to solve problems.

G.GF.7: : Prove that a given quadrilateral is a parallelogram, rhombus, rectangle, square, kite, or trapezoid, and apply these relationships to solve problems.

G.GF.8: : Prove and apply theorems about triangles including:

G.GF.8.1: : Angle-Sum Theorem,

G.GF.8.2: : Exterior Angle Theorem,

G.GF.8.3: : Isosceles Triangle Theorem and its converse,

G.GF.8.6: : Inequality Theorem and its converse, and

G.GF.8.7: : Geometric Mean Theorem.

G.GF.9: : Calculate the perimeter of polygons when given the vertices, including using the distance formula.

3.3: : Geometric Probability

3.3.1: : Students determine probability in geometric contexts.

G.GF.12: : Calculate probabilities as a proportion of area in a geometric context.

G.LA: : Lines & Angles

4.1: : Define & Construct

4.1.1: : Students use precise definitions and various construction tools to create geometric figures.

G.LA.1: : Use precise definitions and standard geometric notation for angles, perpendicular lines, parallel lines, and line segments based on the undefined notions of point, line, and distance along a line.

G.LA.2: : Make formal geometric constructions with a variety of tools and methods including:

G.LA.2.1: : Congruent segments and angles,

G.LA.2.2: : Segment and angle bisectors,

G.LA.2.3: : Perpendicular lines and perpendicular bisectors of a line segment,

G.LA.2.4: : Parallel lines, and

4.2: : Coordinate Geometry

4.2.1: : Students reason about geometric figures using the coordinate plane.

G.LA.4: : Derive the distance and midpoint formulas and use the formulas, including the slope formula, to verify geometric relationships on a coordinate plane.

4.3: : Parallel & Perpendicular Lines

4.3.1: : Students solve problems involving parallel and perpendicular lines.

G.LA.7: : Prove and apply theorems about lines and angles including:

G.LA.7.1: : Vertical angles,

G.LA.7.2: : Angles formed by parallel lines cut by a transversal, and

G.LA.7.3: : Points on a perpendicular bisector.

G.TRF: : Transformations

5.1: : Coordinate Plane

5.1.1: : Students transform figures on the coordinate plane.

G.TRF.1: : Describe rotations, reflections, and translations as functions that take points in the coordinate plane as inputs and give other points as outputs; write in prime notation.

G.TRF.2: : Compare transformations that preserve distance and angle (rotations, reflections, and translations) to those that do not (dilations) to develop definitions for congruence and similarity.

5.2: : Plane

5.2.1: : Students transform figures and make geometric constructions.

G.TRF.3: : Apply understanding of angles, circles, perpendicular lines, parallel lines, and line segments to develop definitions for rotations, reflections, and translations.

G.TRF.5: : Given two congruent figures, identify the sequence of transformations that maps one figure to another.

G.SC: : Similarities & Congruence

6.1: : Similarity

6.1.1: : Students use similarity criteria to solve problems.

G.SC.1: : Given two figures, apply the definition of similarity in terms of a dilation to identify similar figures, proportional sides, and corresponding congruent angles.

G.SC.2: : Develop and apply the criteria of similarity for triangles (AA~, SAS~, and SSS~) to solve problems and prove geometric relationships.

6.2: : Triangle Congruence

6.2.1: : Students apply congruence criteria to solve problems.

G.SC.5: : Develop and apply the criteria for triangle congruence (ASA, SAS, AAS, SSS, and HL) to solve problems and prove geometric relationships.

Correlation last revised: 10/8/2025

Arkansas - Mathematics: Geometry

Academic Standards | Adopted: 2023