# Academic standards list

### Geometry — Mathematics

### Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

### Congruence

TSS.Math.G.G.CO — Conceptual Category: Geometry

Experiment with transformations in the plane.

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, plane,… ♦

Represent transformations in the plane in multiple ways, including technology. Describe transformations as functions that take points in the plane… ♦

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry the shape onto itself. ♦

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. ♦

Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions that… ♦

Understand congruence in terms of rigid motions.

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…

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and…

Explain how the criteria for triangle congruence (ASA, SAS, AAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Prove geometric theorems.

Make geometric constructions.

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic… ♦

### Similarity, Right Triangles, And Trigonometry

TSS.Math.G.G.SRT — Conceptual Category: Geometry

Understand similarity interms of similarity transformations.

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity…

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Prove theorems involving similarity.

Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.

Define trigonometric ratios and solve problems involving triangles.

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios…

Explain and use the relationship between the sine and cosine of complementary angles.

### Circles

TSS.Math.G.G.C — Conceptual Category: Geometry

Understand and apply theorems about circles.

Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context. ♦

Find areas of sectors of circles.

### Expressing Geometric Properties with Equations

TSS.Math.G.G.GPE — Conceptual Category: Geometry

Translate between the geometric description and the equation for a circle.

Know and write the equation of a circle of given center and radius using the Pythagorean Theorem. ♦

Use coordinates to prove simple geometric theorems algebraically.

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Know and use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

### Geometric Measurement and Dimension

TSS.Math.G.G.GMD — Conceptual Category: Geometry

Explain volume and surface area formulas and use them to solve problems.

Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid.… ♦

Know and use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems. ♦

### Modeling with Geometry

TSS.Math.G.G.MG — Conceptual Category: Geometry

Apply geometric concepts in modeling situations.

♦ Academic Standards marked with a diamond are "

*Supporting Content*" within the grade level or course.

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