Question

ABCD is a trapezium in which AB || CD and AD = BC Show that
(1) angleA = angleB
(ii) triangleABC ~=traiangleBAD
from which book is this question???
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Answer 1

GN.that

AB||CD.....also, AD=BC....

TO PROVE:

Angle A= Angle B

also,

∆ABC is congruent to ∆BAD

SOLN:

Construction: Join AC and BD...

now,

IN ∆ABC and ∆BAD

BC=AD(given)

AB=AB (Same Base)

Angle ADB = Angle CBA...

By SAS congruency,

∆ABC IIS CONGRUENT TO ∆CBA

BY CPCT,

Angle A = Angle B...