In the given figure $A O = D O$ and $C O = B O$ . Prove the triangles formed are congruent.

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Solution

1) It can be simply proved
as both $∠ A O B$ and $∠ C O D$
are vertically opposite angles.
$∴ ∠ A O B = ∠ C O D$
2) In $△$ le $A O B$ & $C O D$ , we
have $A O = O D$
$∠ A O B = ∠ C O D$
and $B O = O C$
By SAS congruency
$△ A O B ≅ △ C O D$

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