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

## The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionTo prove that interior angle bisector propertyInterior 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=ABACConstant ⇒ Draw CE || DA to meet BA produced in EAns ⇒ 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=ECBDDC=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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