1. 5.7 Using Congruent Triangles

2. Using Congruent Triangles
Congruent triangles have congruent corresponding parts. So, if you can prove the two triangles are congruent then you know their corresponding parts must be congruent as well.

3. Example 1: Using Congruent Triangles
Explain how you can use the given information to prove that the hang glider parts are congruent.
Since <RQT and <RST are supplementary to congruent angles, then <RQT must be congruent to <RST.

4. Example 1 Continued Prove
At this point we know:
We also know by Reflexive Property of
Congruence
Since two angles and a non-included side are congruent by the AAS Congruence Theorem
Because corresponding parts of congruent triangles are congruent,

5. You try! 1.)Explain how you can prove .
All three pairs of sides are congruent. So, by the SSS Congruence Theorem
. Because corresponding parts of congruent triangles are congruent,

6. Example 2: Using Congruent Triangles for Measurement
Use the following method to find the distance across a river, from point N to point P.
Place a stake at K on the near side so that
Find M, the midpoint of
Locate the point L so that and L, P and M are collinear.

7. Example 2 Continued
So, what you have created looks Like the figure to the right. Explain how this plan allows you to find the distance across the river? ( )

8. Example 3: Planning a Proof Involving Pairs of Triangles
Use the given information to write a plan for a proof.

9. You try!
2.)