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CBSE Class 9 Answered

If non-parallel sides of trapezium are equal. Prove that the trapezium is cyclic.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Draw CE||AD

AECD is a parallelogram

AD=CE (as AECD is a parallelogram )

AD=CB (given)

So, CE = CB 1 = 2(angles opposite to equal angles of a triangle should be equal)

4 + 5 = 180o

But 5 = 1 = 2

4 + 2 = 180o ABCD is cyclic.If the sum of opposite angles of a quadrilateral is 180 o then the quadrilateral should be a cyclic.

Answered by | 04 Jun, 2014, 03:23: PM

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