Download L5 - Proving Triangle Congruence

Chapter 4, Lesson 5
Objective:
Date:
Students will learn to prove triangles are congruent using the SSS, SAS, ASA, AAS, and HL
Postulates
Wups
Identify the congruent triangles in each figure (i.e., write a congruence statement).
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A. Proving Triangles Congruence
 Goal: Prove two Triangles are Congruent.
o How many parts are there in a triangle?
o To do this, we just have to show three ‘strategic’ pairs of corresponding parts are congruent
o We will show 5 methods for doing this.
1. Side – Side – Side
Method
Definition
SSS
Side – Side – Side
Three pairs of corresponding sides
are congruent.
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Representation
Method
Definition
SAS
Side – Angle – Side
Two pairs of corresponding sides
and the INCLUDED angle are
congruent
ASA
Angle – Side –
Angle
Two pairs of corresponding angles
and the INCLUDED side is
congruent.
AAS
Angle – Angle –
Side
Two pairs of corresponding angles
and a corresponding side is
congruent.
HL
Hypotenuse – Leg
Two right triangles are congruent
if their hypotenuse and a pair of
legs are respectively congruent.
Representation
You cannot prove triangles congruent by AAA or SSA! Here’s why…
You can’t use AAA because: http://www.mathopenref.com/congruentaaa.html
You can’t use ASS because: http://www.mathopenref.com/congruentssa.html
Here’s a way to remember … Side-Side-Angle (SSA) can be reversed to get Angle-Side-Side (ASS!)
Don’t say ASS! Don’t use ASS! It’s NOT a congruence property!!!
Don’t use SSA either, because it’s just ASS backwards!!
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B. Examples: State whether each pair of triangles is congruent by SSS, SAS, ASA, AAS, or HL. If not
method exists, state None.
Determine if the triangle are congruent. If so, state how you know and give a triangle congruence statement.
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