M is a point on side BC of a triangle ABC such that AM is the bisector of BAC. Is it true to say that the perimeter of the triangle is greater than 2 AM? Give a reason for your answer.

Name: M is a point on side BC of a triangle ABC such that AM is the bisector of angle BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.
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Description: M is a point on side BC of a triangle ABC such that AM is the bisector of angle BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.

M is a point on side BC of a triangle ABC such that AM is the bisector of angle BAC. Is it true to say that perimeter of the triangle is greater than 2AM ? Give reason for your answer.

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M is a point on side BC of a triangle ABC such that AM is the bisector of $\angle$ BAC. Is it true to say that the perimeter of the triangle is greater than 2 AM? Give a reason for your answer.

Answers (1)

Perimeter of $\triangle$ ABC = AB + BC + AC

In $\triangle$ AMB and $\triangle$ AMC

We know that the sum of two sides of a triangle is greater than the third side.

AB + BM > AM ......(1)

and AC + MC > AM ......(2)

By adding (1) and (2) equation

AB + BM + MC + AC > 2AM

Since, BC = BM + MC

$\therefore$ AB + BC + AC > 2AM

=> Perimeter of $\triangle$ ABC > 2AM

Hence the given statement is true.

Posted by

infoexpert24

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M is a point on side BC of a triangle ABC such that AM is the bisector of BAC. Is it true to say that the perimeter of the triangle is greater than 2 AM? Give a reason for your answer.

Answers (1)

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M is a point on side BC of a triangle ABC such that AM is the bisector of $\angle$ BAC. Is it true to say that the perimeter of the triangle is greater than 2 AM? Give a reason for your answer.