Math, asked by heereshrajpoot94, 2 months ago

AD is the median of a triangle ABC, prove that AB + BC+CA > 2AD
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Answers

Answered by Aryan0123
4

In the above figure,

AD is a median.

We know that

Median of a triangle divides it's side into 2 equal parts.

So,

BD = DC

Sides opposite to equal angles are equal.

∠BAD = ∠CAD

According to Triangle Inequality property,

  • AB + BD > AD          ------ [Equation 1]
  • AC + CD > AD          ------ [Equation 2]

Adding equations 1 and 2,

AB + BD + AC + CD > AD + AD

AB + BD + AC + CD > 2AD

AB + (BD + CD) + AC > 2AD

AB + BC + AC > 2AD

Know more:

★ Triangle Inequality Property states that sum of 2 sides of any triangle is greater than the third side.

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