Question

ΔABC is an isosceles triangle. P, Q and R are the mid-points of the sides BC, CA and AB, respectively. Then ΔPQR is ______.

Options

• an isosceles triangle

• a scalene triangle

• an equilateral triangle

• can’t say

Answer 1

ΔABC is an isosceles triangle. P, Q and R are the mid-points of the sides BC, CA and AB, respectively. Then ΔPQR is an isosceles triangle.

Explanation:

By the midpoint theorem,

Each side of triangle PQR is parallel to a corresponding side of ABC and equal to half its length: 

PQ || AB and PQ = `1/2` AB

PR || AC and PR = `1/2` AC

QR || BC and QR = `1/2` BC

Since ABC is isosceles with AB = AC, we get

PQ = PR

So, PQR is isosceles.