In the given pairs of triangles, applying only the ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

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Solution

In $△ A O D$ and $△ B O C$
$∠ A O D = ∠ B O C$ [vertically opposite angles]
$O D = O C$ [Given]
$∠ A D O = ∠ B C O$ [Given]
$∴ △ A O D ≅ △ B O C$ [by ASA criterion]

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In the given pairs of triangles, applying only the ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

In △AOD and △BOC∠AOD=∠BOC [vertically opposite angles]OD=OC [Given]∠ADO=∠BCO [Given]∴△AOD≅△BOC [by ASA criterion]

In $△ A O D$ and $△ B O C$
$∠ A O D = ∠ B O C$ [vertically opposite angles]
$O D = O C$ [Given]
$∠ A D O = ∠ B C O$ [Given]
$∴ △ A O D ≅ △ B O C$ [by ASA criterion]