Question

In a parallelogram ABCD the angles A and C are obtuse. Points X and Y are taken on the diagonal BD such that the angles angle XAD and angle YCB are right angles. Prove that XA =YC.

Answer 1

Dear Student!

Here is the answer to your query.

Given : ABCD is a parallelogram and AX and CY are perpendicular on diagonal BD

Now In ∆ABX and ∆CDY

⇒ ∠AXB =  ∠CDY = 90°  (Given)

and ∠ABX = ∠CDY  (Alternate opposite angles)

AB = CD  (opposite sides of a ||gm)

∆ABX ≅ ∆CDY  (by AAS congruency criterion)

⇒ AX = CY  (C.P.C.T.)