Prove the Following:

Question

Given: Segment PT ⊥ segment RT, segment SV ⊥ segment QV,

RT = QV, and PQ = SR

Prove: PT = SV

Answer 1

I will not write out the whole 2 column proof for you, but I will give you the necessary pieces.

The trick here is to show that length of PR=length of QS which is done by adding the equal lengths PQ and RS to QR.

Then you have 2 right triangles with hypotenuse and legs equal (so congruent).

Then PT and SV are equal because they are corresponding parts of congruent triangles.