Geometry Help

[matthew042]

I need help on this problem. I have tried it many times and I don't know how to attack it. In the diagram, angle XYZ = angle AXZ = 90 degrees. AX = XY, and angle XZD = angle YZD. Prove that ZD is perpendicular to AY. Thanks everyone.
[attachment=0:3jir4w8q]Picture.jpg[/attachment:3jir4w8q]

 

[mmm4444bot]

… I have tried it many times …

What have you tried?

What are you thinking?

Please show (or at least explain) some effort.

 

[Deleted member 4993]

I need help on this problem. I have tried it many times and I don't know how to attack it. In the diagram, angle XYZ = angle AXZ = 90 degrees. AX = XY, and angle XZD = angle YZD. Prove that ZD is perpendicular to AY. Thanks everyone.
[attachment=0:3ik54t6l]Picture.jpg[/attachment:3ik54t6l]

Outline of proof:

let

ZX and AY intersect at B

ZD and AY intersect at C

mXAY = mXYA = ?

mXZD = mDZY = ?

Then from right triangle XZY

mZXY = 90° - 2?

Then in triangle XAY

(90°- 2?) + 90° + ? + ? = 180°

? = ?

Hence triangles XAB and BZC are similar - hence mZCB = 90°