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Prove that the perimeter of a triangle i...

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

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Given : In `triangle ABC, AD,BE and CF` are altitudes
To prove : AB+BC+CA > AD+BC+CF
Proof : We know that sides opposite to greater angle is greater
In `triangle ABD, angleD = 90^@`
`therefore angleD < angleB`
So, AB > AD_______1
Similarly
BC > BE and CA > CF____2
Adding 1 and 2
AB + BC + CA > AD + BE + CF
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  14. Find the measure of each angle of an equilateral triangle.

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