By applying SAS congruence condition, state which of the following pairs of triangles are congruent. State the result in symbolic form

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Solution

(i) We have
OA = OC
and OB = OD
and $∠ A O B = ∠ C O D$ which are vertically opposite angles.
Therefore by SAS condition, $△ A O B ≅ △ C O D .$
(ii) We have
BD = CD
$∠ A D B = ∠ A D C = 90^{\circ}$
and AD = AD (common)
Therefore by SAS condition, $△ A D B ≅ △ A D C .$
(iii) We have
AB = CD
$∠ B A D = ∠ D C A$
and AC = CA (Common)
Therefore by SAS condition, $△ B A C ≅ △ D C A .$

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