Question

Assertion : Exterior angle bisector property Reason: Prove of interior angle bisector property

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

To prove that interior angle bisector property

Interior angle bisector theorem - The angle bisector of an angle of a triangle divide the opposite side internally in the ratio of the sides containing the angle.

Given $\Rightarrow △ABC$ In which AD is internal bisector of $\angle A$ meet BC in D.

Prove that $\Rightarrow \frac{BD}{DC}=\frac{AB}{AC}$

Constant $\Rightarrow$ Draw CE || DA to meet BA produced in E

Ans $\Rightarrow$ CE || DA

$\Rightarrow \angle 2=\angle 3$ -Alternate interior angle

$\Rightarrow \angle 1=\angle 4$ - Corresponding angle.

$\Rightarrow$ AD is the bisector

$\Rightarrow \angle 1=\angle 2$ - Definition angle bisector

$\Rightarrow \angle 3=\angle 4$ - From upper equations

$\Rightarrow AE=EC$

$\frac{BD}{DC}=\frac{BA}{AE}$ - In $△DCE$ DA || CE by BPT theorem

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

$\therefore$ The interior angle bisector property.

$\Rightarrow$ The interims angle property.

$\therefore$ Both assertion and reason are correct and Reason is the correct explanation for assertion.