Hushar Mulga
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Given below are some triangles and lengths of line segments. Identify, ray PM is the bisector of ∠QPR.

Practice Set 1.2 | Q 1.1 | Page 13

Given below are some triangles and lengths of line segments. Identify, ray PM is the bisector of ∠QPR.

Solution

In ∆ PQR,

PQ = 7, PR = 3, QM = 3.5, and MR = 1.5 ...(Given)

PQ = 7, PR = 3, QM = 3.5, and MR = 1.5 ...(Given)

`"PQ"/"PR" = 7/3` ...(i)

`"QM"/"MR" = 3.5/1.5 = (3.5 × 10)/(1.5 × 10) = 35/15 = 7/3` ...(ii)

From (i) and (ii)

∴ `"PQ"/"PR" = "QM"/"MR"` 

∴ by converse of angle bisector theorem,

∴ Ray PM is the bisector of ∠QPR.

Solution:-

The statement provides information about a triangle PQR and its side lengths and ratios.

It is given that PQ = 7, PR = 3, QM = 3.5, and MR = 1.5.

The statement then shows that PQ/PR = 7/3 and QM/MR = 3.5/1.5 = 7/3.

Using these ratios, it can be deduced that PQ/PR = QM/MR. By the converse of the angle bisector theorem, this means that Ray PM is the bisector of angle QPR.

Chapter 1. Similarity- Practice Set 1.2  – Page 13

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