Prove that a trapezium will be cyclic is its non-parallel sides are equal
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Prove that a trapezium will be cyclic is its non-parallel sides are equal
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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:- 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:
AD=BC
DC=DC [Common]
∠CAD=∠CBD [Angles in the same segment are equal]
AD=BC [Proved above]
ΔADC≅ΔBCD
Therefore, by CPCT
AC=BD
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