maths

$AD∥BC$

$OA=OB$ and $OD=OC$

Line $CD$ and $AB$ intersect

$∴∠AOD=∠BOC$ [Vertically opposite angles]

In $△AOD$ and $△BOC$,

$OA=OB$

$∠AOD=∠BOC$

$∴△AOD≅△BOC$ [SAS Congruence Rule]

$OD=OD$

$⇒∠OAD=∠OBC$ [by CPCT]

But $∠OAD$ and $∠OBC$ form a pair of alternate angles.

If a transversal intersects two lines such that pair of alternate interior angles is equal, then lines are parallel.

$⇒AD∣∣BC$

Answered By

toppr

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