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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.]
 

                    

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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 \angle1, \angleABC be \angle2, \angle EBC be \angle3, \angle BEC be \angle4.

            \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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