Question

ABCD is a square X and Y are points on sides AD and BC respectively such that AX=BX. Prove that BY=AX and ∠BAX =∠ABX​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Given that ABCD is a square, X and Y are points on sides AD and BC respectively such that AY =BX

We have to prove BY = AX and <BAY = <ABX.

Join B and X, A and Y.

Since, ABCD is a square

LDAB = LCBA = 90°

ZXAB =ZYBA = 90°

Now, consider triangle XAB and YBA

We have

LXAB=LYBA = 90° [From (1)]

BX = AY

And AB=BA

[given]

[Common side]

So, by RHS congruence criterion,

we have AXAB=AYBA

Now, we know that corresponding parts of congruent triangles are equal.

.. BY = AX and <BAY = ZABX.

:: Hence proved