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  • ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that (iv) diagonal AC = diagonal BD

Q : 12 ABCD is a trapezium in which  \small AB\parallel CD and \small AD=BC (see Fig. \small 8.23). Show that diagonal AC \small = diagonal BD

[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: 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)

Posted by

seema garhwal

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