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