Question

ABCD is quadrilateral in which all four angles are equal. proof that AB||CD and AD||BC​

Answer 1

Answer:

Step-by-step explanation:

Hey mate here is your answer:

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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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Hope it helps you.

Answer 2

Answer:

Therefore, AD || BC because there interior angles A and B add up to 180°. ... Therefore, AB || CD because there interior angles A and B add up to 180°. Therefore, it is proved that AB ||CD. And AD || BC.