Question

In the given figure, ABCD is a square and
BX = BY. Prove that <DXC = <DYA.​

Answer 1

Step-by-step explanation:

Given :- ABCD is a square.

BX = BY

To Prove :- angle DXC = angle DYA

Proof :- since, BX = BY

and, AB = BC = CD = AD. ..........( side of square) (1)

AB = BC .........( from 1)

subtract BX from both sides.

AB - BX = BC - BX

AB - BY = BC - BX. ....( since, BX = BY)

AY = CX ...........(2)

And, AD = CD .............. (from 1)

now, in ∆DAY AND ∆ DCX

AY = CX

angle DAY = angleDCX. ...........(90°)

DA = DC ...... from (1)

Now, ∆DAY congruent to ∆ DCX by S.A.S CRITERIA

THEN ,

angle DXC = angle DAY

Hence , proved.