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Question

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

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Solution

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

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 ⇒△ABC In which AD is internal bisector of ∠A meet BC in D.

Prove that ⇒BDDC=ABAC

Constant ⇒ Draw CE || DA to meet BA produced in E

Ans ⇒ CE || DA

⇒∠2=∠3 -Alternate interior angle

⇒∠1=∠4 - Corresponding angle.

⇒ AD is the bisector

⇒∠1=∠2 - Definition angle bisector

⇒∠3=∠4 - From upper equations

⇒AE=EC

BDDC=BAAE - In △DCE DA || CE by BPT theorem

⇒BDDC=ABAC

∴ The interior angle bisector property.

⇒ The interims angle property.

∴ Both assertion and reason are correct and Reason is the correct explanation for assertion.

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