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.]

         
 

Answers (1)

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,

             BC=AD            (Given )

             AB=AB            (Common )

       \angle ABC=\angle BAD              (proved in (i)  )

Thus, \small \Delta ABC\cong \Delta BAD              (By SAS rule)

diagonal AC \small = diagonal BD            (CPCT)

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