SOLUTION: complete the proof. given:isosceles triangle MNP with vertex P; isosceles triangle MNQ with vertex Q prove: triangle MQP is congruent to triangle NQP

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Question 1099252: complete the proof. given:isosceles triangle MNP with vertex P; isosceles triangle MNQ with vertex Q prove: triangle MQP is congruent to triangle NQP
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Given: ΔMNP, ΔMNQ are isosceles
To prove:  ΔMQP ≅ ΔNQP

 


 PM ≅ PN                   Legs of isosceles ΔMNP are ≅

∠PMN ≅ ∠PNM               Base angles of isosceles ΔMNP are ≅

∠QMN ≅ ∠QNM               Base angles of isosceles ΔMNQ are ≅ 

∠PMN+∠QMN ≅ ∠PNM+∠QNM    ≅∠s added to ≅∠s are ≅

 ∠PMQ ≅ ∠PNQ              A whole is equal to the sum of its parts

 QM ≅ QN                   Legs of isosceles ΔMNQ are ≅  

ΔMQP ≅ ΔNQP                SAS

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However there is another case to prove, when Q is on the
same side of MN as P.  This case:

 

In this case, the main difference is that you'll need to 
subtract angles instead of adding them in the 4th step. 


Edwin


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

Or, if you use SSS to prove congruency, you don't need two separate cases.

PM and PN are congruent because triangle PMN is isosceles; likewise QM and QN are congruent. And QP is congruent to itself.

Triangles PMQ and PNQ are congruent by SSS.