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Question

ABCD is a trapezium in which AB||CD andAD=BC(see Fig.) .

Show that A=B ( [Hint : Extend AB and draw a line through Cparallel to DA intersecting AB produced at E.]


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Solution

Showing that the A=B:

Given:

The trapezium ABCD in which

AB||CD

AD=BC (non parallel sides of trapezium are equal)

Construction:

Extended AB and draw a line through C parallel to DA intersecting ABproduced atE

ADCE become parallelogram

Solution:.

In parallelogram ADCE

CE=AD (Opposite sides of a parallelogram)

AD=BC(Given)

BC=CE

CBE=CEB (opposite angles of the equal sides)

also,

ADCE

A+CEB=180°(co-interior angle)

A+CBE=180° ( CBE=CEB)

A=180°-CBE------------------------(1)

B+CBE=180°( As Linear pair)

B=180°-CBE-----------------------(2)

From 1 and 2

A=B

Hence the A=B


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