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

$AB=8\ cm, AC=24\ cm, BD=6\ cm$ and $BC=24\ cm$
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Academic Mathematics NCERT Class 10

Given:

$AB=8\ cm, AC=24\ cm, BD=6\ cm$ and $BC=24\ cm$.

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 $\triangle ABC$,

$DC=BC-BD=(24-6)\ cm=18\ cm$

$\frac{BD}{DC}=\frac{6}{18}=\frac{1}{3}$

$\frac{AB}{AC}=\frac{8}{24}=\frac{1}{3}$

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

Therefore,

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

Updated on: 10-Oct-2022

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