### 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.

HS.G-CO.5.ii: Specify a sequence of transformations that will carry a given figure onto another.

#### 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.

1.4.1.2: Tools may include compass and straightedge, string, reflective devices, paper folding or dynamic geometric software.

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.2.ii: Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

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.2.ii: Understand and apply properties of angles for a quadrilateral inscribed in a circle.

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

#### 3.2: Find arc lengths and areas of sectors of circles

HS.G-C.5: Explain and use the formulas for arc length and area of sectors of 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-GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles, parallelograms, trapezoids and kites.

### 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.

5.1.1.1: May use dissection arguments. Cavalieri’s Principle or informal limit arguments.

5.1.1.2: Cavalieri’s Principle: 2D: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas.

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: 9/22/2020

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