Question

3. If ABCD is a quadrilateral in which Z A = 2 B = 2 C = Z D. Prove that AB || DC and
AD || BC. Is ABCD a parallelogram? Give reasons.
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Answer 1

Answer:

like that

Explanation:

Given, AB∥CD, ∠D=2∠B, AD=b, CD=a

Now, AD=b ∴CM=b

and CD=a ∴AM=a

AB∥CD, thus, AMCD is a parallelogram.

∴∠D=∠AMC

∠AMC=2x

In △MCB

2x=∠MCB+∠x( ∵ Exterior angle is equal to sum of opposite interior angle)

=>∠MCB=x

=>∠MCB=∠B=x

∴MB=MC[As sides opposite to equal angles are equal]

Now, AB=AM+MB

=>AB=a+b

solution

Answer 2

Answer:

here's your answer

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Explanation:

hope it helps you