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Question

Suppose the opposite angles of a quadrilateral are equal. Prove that it is a parallelogram.

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Solution

In a quadrilateral ABCD,
A=C and B=D [Given] --- ( 1 )
We know that, sum of interior angles of quadrilateral is 360.
A+B+C+D=360
A+B+A+B=360 [From ( 1 )]
A+B=180
Similarly, C+D=180
Extend DC to E.
C+BCE=180
Hence, BCE=ADC
If BCE=D then,
ADBC [ DC as a transversal] ---( 2 )
We can similarly show ABDC -- ( 4 )
From ( 2 ) and ( 3 ) we have proved that,
ABCDisaparallelogram.

824835_560402_ans_7ab5a3b53d874782ae0b22d66ec98427.png

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