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ABCD is a quadrilateral in which …

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ABCD is a quadrilateral in which AD=BC and angle DAB =CBA prove that : 1. Tiriangle ABD conguent to triangle BAC 2.BD=AC 3.angle ABD = angle BAC

Posted by Ridhima Rana 6 years, 2 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 2 months ago

In {tex}\triangle{/tex}ABC and {tex}\triangle{/tex}BAC
AD = BC [Given]
{tex} \angle {/tex}DAB = {tex} \angle {/tex}CBA [Given]
AB = AB [Common]
{tex}\therefore \triangle ABD \cong \triangle BAC{/tex} [By SAS congruency]
Since
ΔABD≅ΔBAC
{tex}\therefore {/tex} BD=AC[By C.P.C.T.]
Since
ΔABD≅ΔBAC{tex}\triangle \mathrm{ABD} \cong \triangle \mathrm{BAC}{/tex}
{tex}\therefore{/tex}{tex} \angle {/tex}ABD = {tex} \angle {/tex}BAC [By C.P.C.T.]

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