Question

ABCD is a square X is the mid point of AB and Y is the mid point of BC prove that
1. ADX = BAY
2.DXA= AYB​

Answer 1

Given :

• ABCD is a square
• X is mid point of AB
• Y is mid point of BC .

To prove :

• ∠ADX = ∠BAY
• ∠DXA= ∠AYB

Proof :

Since , ABCD is a square

AB = BC

1/2 AB = 1/2 BC

• AX = BY _______(1)

In ∆ADX and ∆BAY

• AD = AB ( sides of square are equal)
• ∠A = ∠B ( each 90° - angles of square)
• AX = BY ( from equation 1)

$\tt \therefore \Delta ADX \cong \Delta BAY$ [SAS congruence criteria]

Hence ,

∠ADX = ∠BAY

$\underbrace{\tt \angle DXA = \angle AYB}_{\tt By\ CPCT}$

Hence proved

Refer to the figure attached .

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Some basic concepts :

• Any two figures are said to be congruent if they are not only similar in shape but also equal in area .

• Congruent figures are always similar.

• Similar figures need not to be congruent .

• If two figures are congruent , then their corresponding parts will be equal to one another .