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P-2 Similarity — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-2 Similarity3 Marks
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Answer

Theorem: The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides.
Therefore, we'll find the ratio for all the triangle. Hence, for
$\begin{array}{l}
\text { (1) } \frac{Q M}{M R}=\frac{3.5}{1.5} \\
=2.33
\end{array}$
And $\frac{ QP }{ PR }=\frac{7}{3}$
$\begin{array}{l}
=2.33 \\
\Rightarrow \frac{ QM }{ MR }=\frac{ QP }{ PR }
\end{array}$
$\Rightarrow \operatorname{In}$ (1), ray PM is a bisector.
(2) $\frac{ RM }{ MQ }=\frac{6}{8}$
$=0.75$
And $\frac{ RP }{ PQ }=\frac{7}{10}$
$\begin{array}{l}
=0.7 \\
\Rightarrow \frac{ RM }{ MQ } \neq \frac{ RP }{ PQ }
\end{array}$
$\Rightarrow$ In (2), ray PM is not a bisector.
$\begin{array}{l}\text { (3) } \frac{R M}{M Q}=\frac{4}{3.6} \\ =1.1 \\ \text { And } \frac{R P}{P Q}=\frac{10}{9} \\ =1.11 \\ \Rightarrow \frac{R M}{M Q}=\frac{R P}{P Q} \\ \Rightarrow \operatorname{In}(3), \text { ray } P M \text { is a bisector. }\end{array}$

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