Question

In a ∆ABC, AB = AC and D is the midpoint of BC. If DM and DN are perpendiculars drawn to AB and AC respectively, prove that DM and DN are equal.​

Answer 1

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In a ∆ABC, AB = AC and D is the midpoint of BC. If DM and DN are perpendiculars drawn to AB and AC respectively, prove that DM and DN are equal.

$\huge\sf \green{\underline{\red{\underline{\blue{\underline{\orange{Given :-}}}}}}}$

In ∆ABC,

1. AB = AC.
2. D is the midpoint of BC.

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If DM & DN are perpendiculars drawn to AB and AC respectively, Then,

• Prove that DM = DN.

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In ∆DMC = ∆DNB

AB = AC 【Given】

∠DMC = ∠DNB 【each 90°】

BD = CD 【D is the mid-point of BC】

∆DMC ≅ ∆DNB 【By SAS congruence theorem】

So,

DM = DN 【By CPCT】

Answer 2

Step-by-step explanation:

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