Question

In the following figure , CD bisects AB and ∠A is equal to ∠B then
(i) Show that ∆AOC ≅ ∆BOD. (ii) Is ∠C=∠D? Give reason.

Answer 1

In triangle AOC and triangle BOD :-
(i) angle CAO = angle DBO (given)
Angle COA = angle DOB ( vertically opposite angles )
AO = BO ( given that CD bisects AB )
And so triangle AOC is congruent to triangle BOD by ASA rule .
And therefore angle C = angle D ( C.P.C.T )
(ii) yes angle C is equal to angle D ( proven above by CPCT)
~Hence Proved~

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