Packet #3 - White Plains Public Schools / Overview

[Pages:65]Triangle Congruence

Packet #3

Name ____________________________ Teacher _____________

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Day 1: Identifying Congruent Triangles

Warm-Up

Five Ways to Prove Triangles Congruent

In previous lessons, you learned that congruent triangles have all corresponding sides and all corresponding angles congruent. Do we need to show all six parts congruent to conclude that two triangles are congruent? The answer is no. We can show triangles are congruent by showing few than all three sides and angles congruent, so long as these congruent sides and angles are in the correct order. The arrangements that prove triangles congruent are as follows:

Side-Side-Side (SSS) Side-Angle-Side (SAS) Angle-Side-Angle (ASA) Angle-Angle-Side (AAS) Hypotenuse-Leg (HL) ? for right triangles only We will take a look at each of these in turn.

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Example 1: Identifying Congruent Triangles

** Challenge**

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Example 2:

The pair of triangles below has two corresponding parts marked as congruent.

1.

4.

Answer: _______ _______ 2.

Answer: _______ ______ 5.

Answer: _______ _____ 3.

Answer: _______ _______ 6.

Answer: _______ _______

Answer: _______ _______ 5

Example 3:

Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, AAS} that can be used to prove the triangles congruent. If not, write not possible. (Hint: Remember to look for the reflexive side and vertical angles!!!!)

The Reflexive Side

Vertical Angles

_________

___________

___________

___________

___________

___________

__________

___________

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The Two That DON'T Work

So far, we have seen that there are four ways to prove a triangle congruent: SSS, SAS, ASA, and AAS. You might be wondering if there are any configurations that don't prove triangles congruent. There are two: AAA and SSA.

Why AAA doesn't work

Given: 1 Can we prove that

Answer: NO. Having all three angles congruent without any congruent corresponding sides will ensure the triangles are similar (same shape), but not necessarily congruent.

Why SSA doesn't work (the "Donkey" Postulate)

Given: Can we prove that

Answer: NO. It is possible to draw two different triangles given two congruent corresponding sides and a nonincluded angle. Therefore, we cannot guarantee that, given SSA, we will have two congruent triangles.

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SUMMARY The Two ThaT DoN'T work: aaa aND SSa

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