SOLUTION: In Triangle ABC, it is given that CA=CB. Points P and Q are marked on segments CA and CB respectively, so that angles CBP and CAQ are the same size. Prove that CP=CQ. Thank you.

Algebra ->  Algebra  -> Triangles -> SOLUTION: In Triangle ABC, it is given that CA=CB. Points P and Q are marked on segments CA and CB respectively, so that angles CBP and CAQ are the same size. Prove that CP=CQ. Thank you.       Log On

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Question 147100: In Triangle ABC, it is given that CA=CB. Points P and Q are marked on segments CA and CB respectively, so that angles CBP and CAQ are the same size. Prove that CP=CQ.
Thank you.
Answer by Edwin McCravy(6935) About Me  (Show Source):
You can put this solution on YOUR website!
In Triangle ABC, it is given that CA=CB. Points P and Q are marked on segments CA and CB respectively, so that angles CBP and CAQ are the same size. Prove that CP=CQ.

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ÐCBP = ÐCAQ      Given

  CA = CB        Given 

  ÐC = ÐC        Identity

DCBP @ DCAQ      Angle-Side-Angle

  CP = CQ        Corresponding parts of congruent triangles

Edwin