Q: 12     ABCD is a trapezium in which   and    (see Fig. ). Show that (i)  [Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

Given: ABCD is a trapezium in which   and

To prove :

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

In AECD,

AE||DC             (Given)

Hence, AECD is a parallelogram.

From 1 and 2, we get

CE=BC

In BCE,

.................3  (opposite angles of equal sides)

...................4(linear pairs)

.....................5(Co-interior angles)

From 4 and 5, we get

(Since,)

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