### HS.G-CO: Congruence

#### 1.1: Experiment with transformations in the plane

HS.G-CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane.

HS.G-CO.2.i: Represent transformations in the plane.

HS.G-CO.2.ii: Describe transformations as functions that take points in the plane as inputs and give other points as outputs.

HS.G-CO.2.iii: Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

HS.G-CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

HS.G-CO.4: Develop or verify experimentally the characteristics of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

HS.G-CO.5.i: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.

#### 1.2: Understand congruence in terms of rigid motions

HS.G-CO.6.i: Use geometric descriptions of rigid motions to predict the effect of a given rigid motion on a given figure.

HS.G-CO.6.ii: Use the definition of congruence in terms of rigid motions to decide if two figures are congruent.

HS.G-CO.8: Prove two triangles are congruent using the congruence theorems such as ASA, SAS, and SSS.

#### 1.3: Prove and apply geometric theorems

HS.G-CO.9: Prove and apply theorems about lines and angles.

HS.G-CO.10: Prove and apply theorems about triangle properties.

HS.G-CO.11: Prove and apply theorems about parallelograms.

#### 1.4: Make geometric constructions

HS.G-CO.12: Make basic geometric constructions with a variety of tools and methods.

HS.G-CO.13: Apply basic constructions to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in circles.

### HS.G-SRT: Similarity, Right Triangles, and Trigonometry

#### 2.1: Understand similarity

HS.G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor.

HS.G-SRT.2.i: Given two figures, use transformations to decide if they are similar.

HS.G-SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

#### 2.2: Prove theorems involving similarity

HS.G-SRT.4: Prove similarity theorems about triangles.

HS.G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

#### 2.3: Define trigonometric ratios and solve problems involving right triangles

HS.G-SRT.6: Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine, and tangent of an acute angle in a right triangle.

HS.G-SRT.8: Use special right triangles (30°-60°-90° and 45°-45°-90°), trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

### HS.G-C: Circles

#### 3.1: Understand and apply theorems about circles

HS.G-C.1: Understand and apply theorems about relationships with line segments and circles including radii, diameter, secants, tangents, and chords.

HS.G-C.2.i: Understand and apply theorems about relationships with angles formed by radii, diameter, secants, tangents, and chords.

HS.G-C.3: Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.

### HS.G-GPE: Expressing Geometric Properties with Equations

#### 4.1: Understand and use conic sections

HS.G-GPE.1.i: Derive the equation of a circle of given center and radius.

HS.G-GPE.1.ii: Derive the equation of a parabola given a focus and directrix.

HS.G-GPE.1.iii: Derive the equations of ellipses and hyperbolas given foci, using the fact that the sum or difference of distances from the foci is constant.

HS.G-GPE.3.i: Identify key features of conic sections given their equations.

HS.G-GPE.3.ii: Apply properties of conic sections in real world situations.

#### 4.2: Use coordinates to verify simple geometric theorems algebraically

HS.G-GPE.5.i: Develop and verify the slope criteria for parallel and perpendicular lines.

### HS.G-GMD: Geometric Measurement and Dimension

#### 5.1: Explain surface area and volume formulas and use them to solve problems

HS.G-GMD.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.

HS.G-GMD.2: Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.

HS.G-GMD.3: Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.

Correlation last revised: 9/24/2019

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