Download Chapter 8 Proving Triangles Congruent

By Shelby Smith and Nellie Diaz
CHAPTER 8
PROVING TRIANGLES CONGRUENT
Section 8-1
SSS and SAS
 If three sides of one triangle are congruent to three sides
of another triangle, then the triangles are congruent.
 If two sides and the included angle of one triangle are
congruent to two sides and the included angle of another
triangle, then the triangles are congruent.
Section 8-2
ASA and AAS
 If two angles and the included side of one triangle are
congruent to two angles and the included side of another
triangle, then the triangles are congruent.
 If two angles and a nonincluded side of one triangle are
congruent to two angles and a nonincluded side of
another triangle, then the triangles are congruent.
Section 8-3
Congruent Triangles
 If the hypotenuse and the leg of one right triangle are
congruent to the hypotenuse and the leg of another right
triangle, then the triangles are congruent.
Hypotenuse Leg (HL)
Identify the Theorem that
goes with each Triangle.
30
60
AAS
60
60
SAS
60
60
60
SSS
SSS
60
Section 8-4
Using Congruent Triangles in
Proofs
 CPCTC
Statements
Reasons
-Corresponding Parts
1.)<A = <C
1.) Given
of Congruent Triangles
2.)BD bisects <ABC
2.) Given
are Congruent.
3.)<1 = <2
3.) Defn. of < bisector
4.) BD = BD
4.) reflexive prop.
Given: <A = <C, BD bisects <ABC
5.) ABD = CBD
5.) AAS
Prove: AB = CB
6.) AB = CB
6.) CPCTC
Section 8-5
Using More than One Pair of
Congruent Triangles
 Some overlapping triangles share a common
angle.