AR.Math.Content.HSG.CO: Congruence

AR.Math.Content.HSG.CO.A: Investigate transformations in the plane.

AR.Math.Content.HSG.CO.A.1: Based on the undefined notions of point, line, plane, distance along a line, and distance around a circular arc, define: angle, line segment, circle, perpendicular lines, parallel lines.

 Circles
 Inscribed Angles
 Parallel, Intersecting, and Skew Lines

AR.Math.Content.HSG.CO.A.2: Represent transformations in the plane (e.g. using transparencies, tracing paper, geometry software, etc.). Describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. (e.g., translation versus dilation).

 Dilations
 Rotations, Reflections, and Translations
 Translations

AR.Math.Content.HSG.CO.A.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and/or reflections that carry it onto itself.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures

AR.Math.Content.HSG.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

 Dilations
 Reflections
 Rotations, Reflections, and Translations
 Translations

AR.Math.Content.HSG.CO.A.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure, (e.g., using graph paper, tracing paper, miras, geometry software, etc.). Specify a sequence of transformations that will carry a given figure onto another.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

AR.Math.Content.HSG.CO.B: Understand congruence in terms of rigid motions.

AR.Math.Content.HSG.CO.B.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

 Absolute Value with Linear Functions
 Circles
 Dilations
 Holiday Snowflake Designer
 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

AR.Math.Content.HSG.CO.B.8: Investigate congruence in terms of rigid motion to develop the criteria for triangle congruence (ASA, SAS, AAS, SSS, and HL).

 Rotations, Reflections, and Translations
 Translations

AR.Math.Content.HSG.CO.C: Apply and prove geometric theorems.

AR.Math.Content.HSG.CO.C.9: Apply and prove theorems about lines and angles.

 Investigating Angle Theorems

AR.Math.Content.HSG.CO.C.10: Apply and prove theorems about triangles.

 Isosceles and Equilateral Triangles
 Polygon Angle Sum
 Triangle Angle Sum
 Triangle Inequalities

AR.Math.Content.HSG.CO.C.11: Apply and prove theorems about quadrilaterals.

 Parallelogram Conditions
 Special Parallelograms

AR.Math.Content.HSG.CO.D: Make geometric constructions.

AR.Math.Content.HSG.CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines

AR.Math.Content.HSG.SRT: Similarity, Right Triangles, and Trigonometry

AR.Math.Content.HSG.SRT.A: Understand similarity in terms of similarity transformations.

AR.Math.Content.HSG.SRT.A.1: Verify experimentally the properties of dilations given by a center and a scale factor. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

 Dilations
 Similar Figures

AR.Math.Content.HSG.SRT.A.2: Given two figures: Use the definition of similarity in terms of similarity transformations to determine if they are similar. Explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

 Circles
 Dilations
 Similar Figures

AR.Math.Content.HSG.SRT.A.3: Use the properties of similarity transformations to establish the AA, SAS~, SSS~ criteria for two triangles to be similar.

 Similar Figures

AR.Math.Content.HSG.SRT.B: Apply and prove theorems involving similarity.

AR.Math.Content.HSG.SRT.B.4: Use triangle similarity to apply and prove theorems about triangles.

 Similar Figures

AR.Math.Content.HSG.SRT.B.5: Use congruence (SSS, SAS, ASA, AAS, and HL) and similarity (AA, SSS~, SAS~) criteria for triangles to solve problems. Use congruence and similarity criteria to prove relationships in geometric figures.

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

AR.Math.Content.HSG.SRT.C: Define trigonometric ratios and solve problems involving right triangles.

AR.Math.Content.HSG.SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

 Sine, Cosine, and Tangent Ratios

AR.Math.Content.HSG.SRT.C.8: Use trigonometric ratios, special right triangles, and/or the Pythagorean Theorem to find unknown measurements of right triangles in applied problems.

 Cosine Function
 Distance Formula
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Tangent Function

AR.Math.Content.HSG.C: Circles

AR.Math.Content.HSG.C.A: Understand and apply theorems about circles.

AR.Math.Content.HSG.C.A.2: Identify, describe, and use relationships among angles, radii, segments, lines, arcs, and chords as related to circles.

 Chords and Arcs
 Inscribed Angles

AR.Math.Content.HSG.C.A.3: Construct the inscribed and circumscribed circles of a triangle. Prove properties of angles for a quadrilateral inscribed in a circle.

 Concurrent Lines, Medians, and Altitudes
 Inscribed Angles

AR.Math.Content.HSG.GPE: Expressing Geometric Properties with Equations

AR.Math.Content.HSG.GPE.A: Translate between the geometric description and the equation for a conic section.

AR.Math.Content.HSG.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Complete the square to find the center and radius of a circle given by an equation.

 Circles

AR.Math.Content.HSG.GPE.A.2: Derive the equation of a parabola given a focus and directrix.

 Parabolas

AR.Math.Content.HSG.GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

 Ellipses
 Hyperbolas

AR.Math.Content.HSG.GMD: Geometric Measurement and Dimension

AR.Math.Content.HSG.GMD.A: Explain volume formulas and use them to solve problems.

AR.Math.Content.HSG.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

 Circumference and Area of Circles
 Prisms and Cylinders
 Pyramids and Cones

AR.Math.Content.HSG.GMD.A.3: Use volume formulas for cylinders, pyramids, cones, spheres, and to solve problems which may involve composite figures. Compute the effect on volume of changing one or more dimension(s).

 Prisms and Cylinders
 Pyramids and Cones

Correlation last revised: 9/8/2017

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