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

$AB=5\ cm, AC=12\ cm, BD=2.5\ cm$ and $BC=9\ cm$
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Given:

$AB=5\ cm, AC=12\ cm, BD=2.5\ cm$ and $BC=9\ cm$

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 $\triangle ABC$,

$DC=BC-BD=(9-2.5)\ cm=6.5\ cm$

$\frac{BD}{DC}=\frac{2.5}{6.5}=\frac{25}{65}=\frac{5}{13}$

$\frac{AB}{AC}=\frac{5}{12}$

$\frac{BD}{DC}≠\frac{AB}{AC}$

Therefore,

$AD$ is not the bisector of $\angle A$.

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Updated on: 10-Oct-2022

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