Question

А
20. In AABC, D is the midpoint of BC. If DL I AB
and DM I AC such that DL = DM, prove that
AB = AC
M
B.
C
no​

Answer 1

Answer:

Therefore, it is proved that AB=AC.

Step-by-step explanation:

It is given that D is the midpoint of BCDL⊥AB and DM⊥AC such that DL=DM

Considering △BLD and △CMD as right angled triangle

So we can write it as

∠BLD=∠CMD=90°

We know that BD=CD and DL=DM

By RHS congruence criterion

△BLD=△CMD

∠ABD=∠ACD(c.p.c.t)

Now, in ∠ABC

∠ABD=∠ACD

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

AB=AC

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