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Triangle And Its Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangle And Its Angles3 Marks
Question
In figure $AE$ bisects $\angle\text{CAD}$ and $\angle\text{B}=\angle\text{C}.$ Prove that $AE\ ||\ BC$.
✓

Answer

Let $\angle\text{B}=\angle\text{C}=\text{x}$
Then, $\angle\text{CAD}=\angle\text{B}+\angle\text{C}=2\text{x}$ (exterior angle)
$\Rightarrow\frac{1}{2}\angle\text{CAD}=\text{x}$
$\Rightarrow\angle\text{EAC}=\text{x}$
$\Rightarrow\angle\text{EAC}=\angle\text{C}$
These are alternate interior angles for the lines $AE$ and $BC$
$\therefore\text{AE }||\text{ BC}$

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