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Q

ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that (iii) ∆ ABC ≅ ∆ BAD

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

(iii) \small \Delta ABC\cong \Delta BAD

[Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

        

Answers (1)
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Given: ABCD is a trapezium in which  \small AB\parallel CD and  \small AD=BC

To prove :\small \Delta ABC\cong \Delta BAD

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)

 

 

 

 

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