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Question

ABCD is a trapezium in which AB || CD and AD =BC (see the given figure). Then, A=B

A
True
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B
False
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Solution

The correct option is A True
Let us extend AB. Then, draw a line through C, which is parallel to AD, intersecting AE at point E. It is clear that AECD is a parallelogram.
AD = CE (Opposite sides of parallelogram AECD)
However, AD = BC (Given)
Therefore, BC = CE
CEB=CBE
CBE+CBA=180 (Linear pair)………….(1)
CBA+DAB=180 (Angles on the same side of transversal)……….(2)
From (1) and (2) A=B

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