Question

ABCD is trapezium in which AB || CD. If AD = BC, show that angle
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Answer 1

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Answer 2

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Given:

ABCD is a trapezium in which AB//CD and AD=BC

To prove:

Angle A= Angle B

Construction:

Extend AB and draw a line through C parallel to DA intersecting AB produced at E

Proof:

AD // CE (from construction)

& AE // DC (As AB // DC, & AB is extended)

In AECD, both pair of opposite sides are parallel,

AECD is a parallelogram.....

.: AD = CE (opposite sides of parallelogram)

But AD = BC (given)

=> BC = CE

so, angle CEB = angle CBE ( In triangle BCE, angle opposite to equal sides are equal) - (1)

For AD//CE

& AE is transversal

angle A + angle CEB = 180* (Interior angle on the same side of transversal is supplementary)

angle A = 180* - angle CEB - (2)

For AE is a line

So, angle B + angle CBE = 180* (Linear pair)

angle B + CEB = 180* (from eq (1))

angle B = 180* - angle CEB - (3)

From (2) & (3)

Angle A = Angle B

Hence Proved....

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