Question

In a ∆ABC, find the measures of the angles of the triangle formed by joining the mid-points of the sides of the triangle.

Answer 1

Given : in triangle ABC triangle formed by joining the mid-points of the sides of the triangles ​

To Find : measures of the angles of the triangle formed

Solution

Let say P , Q & R are mid points of Side  AB , BC & AC

Line segment joining mid point of two sides of Triangle is Half of third side

=> PQ  = AC/2

    QR =  AB/2

     PR  = BC/2

=> PQ/AC = QR/AB = PR/BC = 1/2

=> ΔPQR ≈ ΔACB   ( corresponding sides are proportional )

Corresponding angles of similar triangle are Equal

=> ∠P = ∠A

    ∠Q = ∠C

     ∠R = ∠B

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