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In ABC, D is the midpoint of BC. If DL AB and DM AC such th

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In $△ A BC, D$ is the midpoint of $BC$ . If $D L ⊥ A B$ and $D M ⊥ A C$ such that $D L = D M$ , prove that $A B = A C$ .

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△ A BC, D

is the midpoint of

BC

. If

D L ⊥ A B

and

D M ⊥ A C

such that

D L = D M

, prove that

A B = A C

15 mins ago

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Text solutionVerified

It is given that

D

is the midpoint of

BC D L ⊥ A B

and

D M ⊥ A C

such that

D L = D M

Considering

△ B L D

and

△ CM D

as right angled triangle

So we can write it as

∠ B L D = ∠ CM D = 9 0^{\circ}

We know that

B D = C D

and

D L = D M

R H S

congruence criterion

△ B L D = △ CM D

∠ A B D = ∠ A C D (c . p . c . t)

Now, in

∠ A BC

∠ A B D = ∠ A C D

We know that the sides opposite to equal angles are equal so we get

A B = A C

Therefore, it is proved that

A B = A C

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Question Text	In $△ A BC, D$ is the midpoint of $BC$ . If $D L ⊥ A B$ and $D M ⊥ A C$ such that $D L = D M$ , prove that $A B = A C$ .
Answer Type	Text solution:1
Upvotes	150

In △ABC,D is the midpoint of BC. If DL⊥AB and DM⊥AC such that DL=DM, prove that AB=AC.

Text solutionVerified

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In $△ A BC, D$ is the midpoint of $BC$ . If $D L ⊥ A B$ and $D M ⊥ A C$ such that $D L = D M$ , prove that $A B = A C$ .