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.]

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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  $\small \Delta ABC\, \, and\, \, \, \Delta BAD$,

AB=AB            (Common )

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

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

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