Question

ABCD is a quadrilateral in which all the four angle are equal show that WB=BC andAB=CD​

Answer 1

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Step-by-step explanation:

Solution:-

Given,

ABCD is a quadrilateral

Angles A=B=Ç=D

To Prove,

AB || CD and AD || BC

Proof:- Here,

angle A+B+Ç+D=360° [angle sum property of quadrilaterals]

=>A+A+A+A=360°

=>4A=360°

=>A=90° ……[equation 1]

Again, angle A+B=180°

Therefore, angles A and B are linear

And also they are adjacent.

Therefore, AD || BC because there interior angles A and B add up to 180°.

Similarly, angle A+D=180°

Therefore, angles A and D are linear

And also they are adjacent.

Therefore, AB || CD because there interior angles A and B add up to 180°.

Therefore, it is proved that AB ||CD

And AD || BC.