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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