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PROVE THAT NON ISOSCELES TRAPEZIUMS ARE NOT CYCLIC

Given: A cyclic quadrilateral ABCD such that AD = BC

To Prove: AB parallel to CD

Construction: Join BD

Proof:

We have AD = BC

Arc DA = Arc BC

Measure of arc DA = Measure of Arc BC

2<2 = 2<1

<2 = <1

The angles <1, <2 are alternate interior angles.

Therefore, AB parallel to CD

Here ABCD is an isosceles trepezium.

ie, NON ISOSCELES TRAPEZIUMS ARE NOT CYCLIC