5 7 Using Congruent Triangles Using Congruent Triangles

5. 7 Using Congruent Triangles

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.

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.

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

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, . .

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.

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? ( )

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

You try! 2. )