Question

ABCD is a quadrilateral in which all four angles are equal. Show that AB is parallel to CD and AD is parallel to BC​

Answer 1

Given,

ABCD is a quadrilateral

Angles A=B=C=D

To Prove,

AB || CD and AD || BC

Proof:- Here,

angle A+B+C+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.

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Answer 2

Refer to the attachment:-

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