Curriculum Framework

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.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.9: Apply and prove theorems about lines and angles.

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.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.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.

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.

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

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.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.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.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.

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

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.

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: 1/22/2020