# Q : 12     ABCD is a trapezium in which  $\small AB\parallel CD$ and $\small AD=BC$ (see Fig. $\small 8.23$). Show that(iv) diagonal AC $\small =$ diagonal BD[Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

S seema garhwal

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

To prove: diagonal AC $\small =$ diagonal BD

Proof: In  $\small \Delta ABC\, \, and\, \, \, \Delta BAD$,

$\angle ABC=\angle BAD$              (proved in (i)  )
Thus, $\small \Delta ABC\cong \Delta BAD$              (By SAS rule)
diagonal AC $\small =$ diagonal BD            (CPCT)