In the given figure, AY⊥ ZY and BY ⊥ XY, such that AY = ZY and BY = XY. Prove that AB=ZX

Given AY = ZY ; AY⊥ZY

and BY = XY;BY⊥XY

To prove AB = ZX

Proof ∵BY⊥ XY and AY ⊥ ZY

∴∠BYX = 90°

and ∠AYZ = 90°

=>∴BYX =∴AYZ

On adding∠AYX both sides, we get

∠BYX+ ∠AYX =∠AYZ + ∠AYX

=> ∠AYB = ∠ZYX

Now, in ∆AYB and ∆ZYX, we have

AY = ZY

BY = XY

and ∠AYB = ∠ZYX [proved above]

[by SAS congruence rule]

AB = ZX