## Symbols Toolbox

Congruent Triangles and their corresponding parts

## Definitions, Postulates, and Theorems

**Triangle Sums**

- Interior Angles
- Vertex
- Triangle Sum Theorem
- Exterior Angle
- Exterior Angle Sum Theorem
- Remote Interior Angles
- Exterior Angle Theorem

**Congruent Figures**

- Congruent Triangles
- Congruence Statements
- Third Angle Theorem
- Reflexive Property of Congruence
- Symmetric Property of Congruence
- Transitive Property of Congruence

**Triangle Congruence using SSS and SAS**

- Side-Side-Side (SSS) Triangle Congruence Postulate
- Included Angle
- Side-Angle-Side (SAS) Triangle Congruence Postulate
- Distance Formula

**Triangle Congruence using ASA, AAS, and HL**

- Angle-Side-Angle (ASA) Congruence Postulate
- Angle-Angle-Side (AAS) Congruence Theorem
- Hypotenuse
- Legs (of a right triangle)
- HL Congruence Theorem

**Isosceles and Equilateral Triangles**

- Base
- Base Angles
- Vertex Angle
- Legs (of an isosceles triangle)
- Base Angles Theorem
- Isosceles Triangle Theorem
- Base Angles Theorem Converse
- Isosceles Triangle Theorem Converse
- Equilateral Triangles Theorem

## Review

For each pair of triangles, write what needs to be congruent in order for the triangles to be congruent. Then, write the congruence statement for the triangles.

- HL
- ASA
- AAS
- SSS
- SAS

Using the pictures below, determine which theorem, postulate or definition that supports each statement below.

- If , then

## Texas Instruments Resources

*In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9689.*