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ASA Criteria for Congruency

In the follow...

Question

In the following figure, it is given that $A B ∥ D E$ and $B C = E C . △ A B C ≅ △ D E C$ by ___ congruence rule.

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Solution

In $△ A B C$ and $△ D E C,$

$B C = E C$ [given]
$∠ A B C = ∠ D E C$ [alternate interior angles]
$∠ A C B = ∠ D C E$ [vertically opposite angles]

Therefore, $△ A B C ≅ △ D E C$ [by ASA congruence condition]

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