In figure below, check whether AD is the bisector $\angle A$ of $\triangle ABC$ in each of the following:

$AB=4\ cm, AC=6\ cm, BD=1.6\ cm$ and $CD=2.4\ cm$
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Given:

$AB=4\ cm, AC=6\ cm, BD=1.6\ cm$ and $CD=2.4\ cm$.

To do: We have to check whether AD is the bisector of $\angle A$ in $\triangle ABC$.

Solution: 

We know that,

The angle bisector theorem states that an angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

In $\triangle ABC$,

$\frac{BD}{DC}=\frac{1.6}{2.4}=\frac{16}{24}=\frac{2}{3}$

$\frac{AB}{AC}=\frac{4}{6}=\frac{2}{3}$

$\frac{BD}{DC}=\frac{AB}{AC}$

Therefore,

$AD$ is the bisector of $\angle A$.

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Updated on: 10-Oct-2022

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