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ASA Criteria for Congruency

In the follow...

Question

In the following figure, BL =CM. Prove that AD is a median of $△ A B C$

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Solution

In $△ L B D a n d M C D$
$∠ B L D$ = $∠ C M D$
$∠ L D B$ = $∠ M D C$
so, $∠ D B L$ = $∠ D C M$
and BL=CM
then, $△ L B D$ is congruent to $△ M C D$ [ asa congruency]
so, BD=DC [cpctc.]
therefore, AD is a median of $△ A B C$

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