In Fig., OA = OB and OD = OC. Show that 1. AOD BOC 2. AD || BC - Vidyadip

Question

In Fig., OA = OB and OD = OC. Show that

$\triangle$ AOD $\cong$ $\triangle$ BOC
AD || BC

✓

Answer

You may observe that in $\triangle$ AOD and $\triangle$ BOC,
OA = OB (Given)
OD = OC
Also, since $\angle$ AOD and $\angle$ BOC form a pair of vertically opposite angles,
we have $\angle$ AOD = $\angle$ BOC
So, $\triangle$ AOD $\cong$ $\triangle$ BOC (by the SAS congruence rule)
In congruent triangles AOD and BOC, the other corresponding parts are also equal.
So, $\angle$ OAD = $\angle$ OBC and these form a pair of alternate angles for line segments AD and BC.
Therefore, AD || BC

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