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Question
Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.
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Solution
In ∆ PQR,
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.
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