Q15 of 97 Page 205

In an isosceles ∆ABC, AB=AC and the bisectors of ∠B and ∠C intersect each other at O. Also, O and A are joined.

Prove that: (i) OB=OC (ii) ∠OAB=∠OAC


From the given figure, we have:

(i) In ∆ABO and ∆ACO


AB = AC (Given)


AO = AO (Common)


∠ ABO = ∠ ACO


∴ By SAS congruence rule



OB = OB (By CPCT)


(ii) As, By SAS congruence rule


∆ABO ≅ ∆ACO


∴ ∠ OAB = ∠ OAC (By Congruent parts of congruent triangles)


Hence, proved


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Prove that ∠CAD=∠CBD and ∠ADC=∠BCD.


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Each question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.











Assertion (A)



Reason (R)



Each angle of an equilateral triangle is 60°.



Angles opposite to equal sides of a triangle are equal.