Question

If two opposite sides of a cyclic quadrilateral are equal then the other two sides are parallel

Answer 1

Given: Cyclic quadrilateral ABCD such that AD = BC

To Prove: AB parallel to CD

Construction: Join BD

Proof:

Given that AD = BC

Arc DA = Arc BC

∠2 = ∠1 [Equal chords subtend equal angles at the circumference of the circle]

The angles ∠1and ∠2 are alternate interior angles.

Therefore, AB is parallel to CD.

Answer 2

AnswEr:

$\star$ $\sf\underline\pink{Given:-}$

A cyclic quadilateral ABCD such that AD = BC

$\star$ $\sf\underline\orange{To\:prove:-}$

AB || CD.

$\star$ $\sf\underline\red{Construction:-}$

Join BD

$\star$ $\sf\underline\purple{Proof:-}$

We have,

AD = BC

$\implies$ DA = BC

$\implies$ m ( DA ) = m ( BC )

$\implies$ 2$\angle$2=2$\angle$1

$\implies$ $\angle$2=$\angle$1

But, these are alternate interior angles. Therefore, AB || CD.

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#BAL

#Answerwithquality