Chapter 4: Triangles and Congruence
Introduction
In this chapter, you will learn all about triangles. First, we will learn about the properties of triangles and the angles within a triangle. Second, we will use that information to determine if two different triangles are congruent. After proving two triangles are congruent, we will use that information to prove other parts of the triangles are congruent as well as the properties of equilateral and isosceles triangles.
 4.1.
Triangle Sum Theorem
 4.2.
Exterior Angles Theorems
 4.3.
Congruent Triangles
 4.4.
Congruence Statements
 4.5.
Third Angle Theorem
 4.6.
SSS Triangle Congruence
 4.7.
SAS Triangle Congruence
 4.8.
ASA and AAS Triangle Congruence
 4.9.
HL Triangle Congruence
 4.10.
Isosceles Triangles
 4.11.
Equilateral Triangles
Chapter Summary
Summary
This chapter begins with the Triangle Sum Theorem, showing that the sum of the angles in a triangle is a constant. The definition of congruency is presented and from that foundation the chapter presents other important theorems related to congruent triangles, such as the Third Angle Theorem and the SSS, SAS, ASA, AAS and HL Triangle Congruency Theorems.
Chapter Keywords
 Interior Angles
 Vertex
 Triangle Sum Theorem
 Exterior Angle
 Exterior Angle Sum Theorem
 Remote Interior Angles
 Exterior Angle Theorem
 Congruent Triangles
 Third Angle Theorem
 Reflexive Property of Congruence
 Symmetric Property of Congruence
 Transitive Property of Congruence
 SideSideSide (SSS) Triangle Congruence Postulate
 Included Angle
 SideAngleSide (SAS) Triangle Congruence Postulate
 AngleSideAngle (ASA) Congruence Postulate
 AngleAngleSide (AAS or SAA) Congruence Theorem
 HL Congruence Theorem
 Base Angles Theorem
 Isosceles Triangle Theorem
 Base Angles Theorem Converse
 Isosceles Triangle Theorem Converse
 Equilateral Triangles Theorem
Chapter 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*}
m∠1+m∠2=180∘ 
\begin{align*}\angle 5 \cong \angle 6\end{align*}
∠5≅∠6 
\begin{align*}m \angle 1=m \angle 4+ m \angle 3\end{align*}
m∠1=m∠4+m∠3 
\begin{align*}m \angle 8 = 60^\circ\end{align*}
m∠8=60∘ 
\begin{align*}m \angle 5+m \angle 6+m \angle 7=180^\circ\end{align*}
m∠5+m∠6+m∠7=180∘ 
\begin{align*}\angle 8 \cong \angle 9 \cong \angle 10\end{align*}
∠8≅∠9≅∠10  If \begin{align*}m \angle 7 = 90^\circ\end{align*}
m∠7=90∘ , then \begin{align*}m \angle 5 = m \angle 6 = 45^\circ\end{align*}m∠5=m∠6=45∘
Texas Instruments Resources
In the CK12 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.