Question

in the given figure ay is perpendicular to zy and by is perpendicular to xy such that ay=zy and by=xy. prove that ab=zx​

Answer 1

Answer:

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]

image

[by SAS congruence rule]

AB = ZX