Question

11. In the given figure, ABCD is a quadrilateral in which AB || DC and ad||bc



Prove that ADC = ABC.

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Answer 1

$\LARGE{\underline{\underline{\red{\sf{Question:}}}}}$

In the given figure, ABCD is a quαdrilαterαl in which AB || DC αnd αd || bc

Prove thαt ADC = ABC.

$\LARGE{\underline{\underline{\red{\sf{Diagram:}}}}}$

• Attached

$\mathfrak{\purple{Given}}\begin{cases} \sf{ AB\; ||\; CD} \\ \sf AD\;||\;BC \end{cases}$

$\mathfrak{\purple{To \; Prove}} : \underline{\sf{ ADC = ABC }}$

We hαve to drαw AC diαgonαlly

∆ABC αnd ∆ADC

$\implies \sf{AD = BC _{\pink{(opposite \; side)}}}$

$\implies \sf{AB = CD _{\pink{(opposite \; side)}}}$

$\implies \sf{AC = AC _{\pink{(common \; side)}}}$

$\sf{\triangle ABC\; \cong \; \triangle ADC_{\pink{ (S.S.S)}}}$

$\sf{ \therefore angle \; ABC= angle \; ADC}$

$\star \; \huge{\blue{\sf{\underline{Hence, proved}}}}$