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Standard IX

Mathematics

Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

In the figure...

Question

In the figure Point $Q$ is on the side of $M P$ such that $M Q = 2$ and $M P = 5.5$ . Ray $N Q$ is the bisector of $∠ M N P$ of $△ M N P$ . If $M N : N P$ is $k : l$ ,then find $k + l$

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Solution

Given: NQ bisects $∠ M N P$
$M Q = 2$
$M P = 5.5$
$M Q + Q P = 5.5$
$2 + Q P = 5.5$
$Q P = 3.5$
In $△ M N P$ ,
$\frac{M N}{N P} = \frac{M Q}{Q P}$ (By Angle bisector theorem)
$\frac{M N}{N P} = \frac{2}{3.5}$
$\frac{M N}{N P} = \frac{4}{7}$

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In fig, point $Q$ is on the side $M P$ such that $M Q = 2$ units and $M P = 5.5$ units
Ray $N Q$ is the bisector of $∠ M N P$ of $M N P$ . Find $M N : N P$

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Q. In figure ,

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In the figure Point Q is on the side of MP such that MQ=2 and MP=5.5. Ray NQ is the bisector of ∠MNP of △MNP. If MN:NP is k:l,then find k+l

Given: NQ bisects ∠MNPMQ=2MP=5.5MQ+QP=5.52+QP=5.5QP=3.5In △MNP,MNNP=MQQP (By Angle bisector theorem)MNNP=23.5MNNP=47

In the figure Point $Q$ is on the side of $M P$ such that $M Q = 2$ and $M P = 5.5$ . Ray $N Q$ is the bisector of $∠ M N P$ of $△ M N P$ . If $M N : N P$ is $k : l$ ,then find $k + l$

Given: NQ bisects $∠ M N P$
$M Q = 2$
$M P = 5.5$
$M Q + Q P = 5.5$
$2 + Q P = 5.5$
$Q P = 3.5$
In $△ M N P$ ,
$\frac{M N}{N P} = \frac{M Q}{Q P}$ (By Angle bisector theorem)
$\frac{M N}{N P} = \frac{2}{3.5}$
$\frac{M N}{N P} = \frac{4}{7}$