# 4.6: Chapter 4 Review

Difficulty Level:

**At Grade**Created by: CK-12
**Definitions, Postulates, and Theorems**

- Interior Angles
- The angles inside of a closed figure with straight sides.

- Vertex
- The point where the sides of a polygon meet.

- Triangle Sum Theorem
- The interior angles of a triangle add up to \begin{align*}180^\circ\end{align*}.

- Exterior Angle
- The angle formed by one side of a polygon and the extension of the adjacent side.

- Exterior Angle Sum Theorem
- Each set of exterior angles of a polygon add up to \begin{align*}360^\circ\end{align*}.

- Remote Interior Angles
- The two angles in a triangle that are not adjacent to the indicated exterior angle.

- Exterior Angle Theorem
- The sum of the remote interior angles is equal to the non-adjacent exterior angle.

- Congruent Triangles
- Two triangles are congruent if the three corresponding angles and sides are congruent.

- Third Angle Theorem
- If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also congruent.

- Reflexive Property of Congruence
- Any shape is congruent to itself.

- Symmetric Property of Congruence
- If two shapes are congruent, the statement can be written with either shape on either side of the \begin{align*}\cong\end{align*} sign.

- Transitive Property of Congruence
- If two shapes are congruent and one of those is congruent to a third, the first and third shapes are also congruent.

- Side-Side-Side (SSS) Triangle Congruence Postulate
- If three sides in one triangle are congruent to three sides in another triangle, then the triangles are congruent.

- Included Angle
- When an angle is between two given sides of a triangle (or polygon).

- Side-Angle-Side (SAS) Triangle Congruence Postulate
- If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.

- Angle-Side-Angle (ASA) Congruence Postulate
- If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent.

- Angle-Angle-Side (AAS or SAA) Congruence Theorem
- If two angles and a non-included side in one triangle are congruent to two corresponding angles and a non-included side in another triangle, then the triangles are congruent.

- HL Congruence Theorem
- If the hypotenuse and leg in one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are congruent.

- Base Angles Theorem
- The base angles of an isosceles triangle are congruent.

- Isosceles Triangle Theorem
- The angle bisector of the vertex angle in an isosceles triangle is also the perpendicular bisector to the base.

- Base Angles Theorem Converse
- If two angles in a triangle are congruent, then the opposite sides are also congruent.

- Isosceles Triangle Theorem Converse
- The perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle.

- Equilateral Triangles Theorem
- all sides in an equilateral triangle have exactly the same length.

## 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.

- \begin{align*}m \angle 1+m \angle 2=180^\circ\end{align*}
- \begin{align*}\angle 5 \cong \angle 6\end{align*}
- \begin{align*}m \angle 1=m \angle 4+ m \angle 3\end{align*}
- \begin{align*}m \angle 8 = 60^\circ\end{align*}
- \begin{align*}m \angle 5+m \angle 6+m \angle 7=180^\circ\end{align*}
- \begin{align*}\angle 8 \cong \angle 9 \cong \angle 10\end{align*}
- If \begin{align*}m \angle 7 = 90^\circ\end{align*}, then \begin{align*}m \angle 5 = m \angle 6 = 45^\circ\end{align*}

## 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.*

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Tags:

angle theorems
CK.MAT.ENG.SE.1.Geometry-Basic.4
CK.MAT.ENG.SE.2.Geometry.4
(11 more)
congruent figures
equilateral triangles
Exterior Angles Theorem
isosceles triangles
properties of congruence
Third Angle Theorem
triangle congruence
triangle congruence postulates
Triangle Sum Theorem
triangle sums
triangles

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Date Created:

Feb 22, 2012
Last Modified:

Feb 03, 2016
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