Thread: In desperate need of help! 3 Problems

My Discrete exam is coming up in two days and I just realized that I didn't copy down solutions for a really hard proofs test that I had. These are three questions that I had no idea how to do on my test. Please help!

1. Given: ABCD is a parallelogram with equilaterals ABF and ADE drawn on sides AB and AD, respectively. Prove that triangle FCE is equilateral.

2. P is any point on rectangle ABCD. Prove that PA^2 + PC^2 = PB^2 + PD^2

3. In triangle ABC, altitude BE is extended to G so that EG = the measure of altitude CF. A line through G and parallel to AC meets BA extended at H, as shown in the figure. Prove that AH = AC.

Diagrams are attached (in order)! Thanks alot!

For the first one

, but

For the second one

Draw a line through such that cuts and orthogonally.

Then play with Pythagorean Theorem.

Finally, for the third one, I'll give you a

Hint

Note that and

Make a fusion with this equalities to get what you want.

See ya