Question

Prove that the triangle formed by joining the midpoints of sides of a right angled triangle is also a right angled triangle.​

Answer 1

Answer:

If we join the any two midpoints of two sides of an isosceles triangle then the line is half of its parallel side of the triangle. So The triangle formed by joining the mid -points of the sides of a right triangle also have one right angle, therefore the triangle is right angle triangle

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Answer 2

Answer:

The line segment joining the midpoints of two sides of any triangle is parallel to the third side (and equal to one-half of it).

Proof of this statement: From the midpoint K of the side AB of a triangle ABC draw parallels to sides BC and CA, respectively meeting sides AC and BC at points L and M. Triangles AKL and KBM are congruent by A-S-A; therefore AL = KM and KL = BM. Also, KLCM is a parallelogram; therefore KM = LC and KL = MC. It follows that AL = LC and BM = MC, .e. that L and M are the midpoints of AC and BC.

It follows that the angles of the triangle KLM formed by the lines joining the midpoints of the sides of another triangle ABC are equal to the angles of that other triangle, and in particular that if one of the latter is right, so is one of the former

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