Question

If the altitude from one vertex of a triangle bisects the opposite side, then prove that the triangle is isosceles

please answer it fast​

Answer 1

Step-by-step explanation:

if the angle bisector is from vertex A to side BC meeting it in, say P, then by the angle bisector theorem AB/AC=BP/PC. If P happens to be the mid-point of BC then BP=PC which makes AB =AC and the triangle is isosceles. Further, if BC =AB=AC then the triangle can be equilateral.

Answer 2

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Let's take an eg. of triangle abc,

If the angle bisector is from vertex A to side BC meeting it in, say P, then by the angle bisector theorem AB/AC=BP/PC. If P happens to be the mid-point of BC then BP=PC which makes AB =AC and the triangle is isosceles. Further, if BC =AB=AC then the triangle can be equilateral.

Hence proved.. ✅

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