Question

the median line AM of the triangle ABC is half the length of the side towards which it is drawn, line BC. prove that triangle ABC is a right triangle.

Answer 1

the median line AM of the triangle ABC is half the length of the side towards which it is drawn, line BC. prove that triangle ABC is a right triangle.

Answer 2

`\\ \sf\longmapsto AM=(1)/(2)BC`

`\\ \sf\longmapsto AM=BM=CM`

• All points are equidistant from M

If it becomes a inscribed triangle

• A,B,C will create a arc of 180°

`\\ \sf\longmapsto arcABC=180°`

• The measure of inscribed angle is half the inscribed arc

`\\ \sf\longmapsto <BAC=(1)/(2)arc ABC`

`\\ \sf\longmapsto <BAC=(1)/(2)180°`

`\\ \sf\longmapsto <BAC=90°`

Hence ABC is a right angled triangle (Verified)