geometric proofs

[troy_jeremy]

This is my problem:

I am given a picture of an isosceles triangle ABC. BC is its base. Inside of the triangle is an X with one line extending from angle C and one extending from angle B. CD and BE intersect at point P.

Given: Triangle ABC is isosceles with AB = AC
D is the midpoint of AB
E is the midpoint of AC
How do I prove that triangle PBC is isosceles?

 

[stapel]

Is "X" a point, or do you just mean that two line segments cross in the interior of the triangle?

Thank you.

Eliz.

 

[troy_jeremy]

"X" is a point where BE and CD intersect

 

[pka]

ΔBCD is congruent to ΔCBE.
So angles \(\displaystyle \angle PCB \cong \angle PBC\)

Base angles do it!

 

[troy_jeremy]

Thanks a bunch!