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.

$Midpoint Theorem Problem$

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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