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# ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that (ii) ∠ C = ∠ D

Q : 12         ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that

(ii) $\small \angle C=\angle D$

[Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

Views

Given: ABCD is a trapezium in which  $\small AB\parallel CD$ and  $\small AD=BC$

To prove :$\small \angle C=\angle D$

Proof:   Let $\angle$ A be $\angle$1, $\angle$ABC be $\angle$2, $\angle$ EBC be $\angle$3, $\angle$ BEC be $\angle$4.

$\angle 1+\angle D= 180 \degree$       (Co-interior angles)

$\angle 2+\angle C= 180 \degree$            (Co-interior angles)

$\therefore \angle 1+\angle D=\angle 2+\angle C$

Thus, $\small \angle C=\angle D$                (Since ,$\small \angle 1=\angle 2$ )

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