Question

In Fig,

AB = AC and AD is the bisector of ∠BAC.
(i) State three pairs of equal parts in triangles ADB and ADC.
(ii) Is ∆ADB ≅ ∆ADC? Give reasons.
(iii) Is ∠B = ∠C? Give reasons.

Answer 1

(i) The three pairs of equal parts are as follows:
AB = AC...................(Given)
∠BAD = ∠CAD......(AD bisects ∠BAC) and
AD = AD..................(common)

(ii) Yes, ∆ADB ≅ ∆ADC.....(By SAS congruence rule)

(iii) ∠B = ∠C.........................(Corresponding parts of congruent triangles)