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.Com
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(20063)   (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.



ÐCBP = ÐCAQ      Given

  CA = CB        Given 

  ÐC = ÐC        Identity

DCBP @ DCAQ      Angle-Side-Angle

  CP = CQ        Corresponding parts of congruent triangles

Edwin
RELATED QUESTIONS

Suppose that ABC is a triangle in which CA > CB. Construct P between C and A so that... (answered by ikleyn)
In triangle ABC, angle B=67° and angle C=46° prove that line CA=line... (answered by ikleyn)
In triangle ABC where B=67 and C=46 prove that... (answered by ikleyn)
In isosceles triangle ABC, CA~=CB. If D is a point on AC between A and C, prove... (answered by ikleyn)
Consider Triangle ABC. A circle k passes through points A and B and intersects CA and CB... (answered by math_helper)
If point C is (-1,-4) and point A is (7,4), find the coordinates of point B on CA such... (answered by ikleyn)
In triangle ABC, D is a point on segment AC and E is a point on CB such that DE and AB... (answered by KMST,solver91311,ikleyn)
How do you find out if two triangles are similar? I know that the triangles' angles must... (answered by solver91311)
In triangle ABC ,angle ACB is 90 degrees and CD is perpendicular to AB.Prove... (answered by jojo14344)