# Midpoint Theorem Problem

Here we will learn how to solve different types of midpoint theorem problem.

 In the adjoining figure, find (i) ∠QPR, (ii) PQ if ST = 2.1 cm.

Solution:

In ∆PQR, S and T are the midpoints of PR and QR respectively.

Therefore, ST = $$\frac{1}{2}$$PQ and ST ∥ PQ.

(i) ∠QPR = ∠RST (Corresponding angles),

i.e., ∠QPR = 55°.

(ii) PQ = 2 × ST = 2 × 2.1 cm = 4.2 cm.

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