Question

Prove that a trapezium will be cyclic is its non-parallel sides are equal​

Answer 1

Answer:

Answer. Question :- Prove that in a cyclic trapezium the non parallel sides are equal. Answer :- Let ABCD be the cyclic trapezium in which AB||CD. Also chord AD subtends ∠ABD and chord BC subtends ∠BDC on the circle at B and D respectively.

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Answer 2

Answer:- Here,

Hey mate,

In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal.

In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal.Let ABCD be the cyclic trapezium in which AB∣∣DC, AC and BD are the diagonals.

Required to prove:

(i) AD=B

(ii) AC=BD

Proof:

• It’s seen that chord AD subtends ∠ABD and chord BC subtends ∠BDC at the circumference of the circle.

• But, ∠ABD=∠BDC [Alternate angles, as AB∣∣DC with BD as the transversal]

• So, Chord AD must be equal to chord BC.

AD=BC

• Now, in ΔADC and ΔBCD

DC=DC [Common]

∠CAD=∠CBD [Angles in the same segment are equal]

AD=BC [Proved above]

• Hence, by SAS criterion of congruence

ΔADC≅ΔBCD

Therefore, by CPCT

AC=BD

Good day,

Thanks:)