Question

In Fig, AD = CD and AB = CB.

(i) State the three pairs of equal parts in ∆ABD and ∆CBD.
(ii) Is ∆ABD ≅ ∆CBD? Why or why not?
(iii) Does BD bisect ∠ABC? Give reasons.

Answer 1

(i) In ∆ABD and ∆CBD, the three pairs of equal parts are as given below:
AB =CB.....................(Given)
AD =CD...................(Given) and
BD =BD....................(Common in both)

(ii) From (i) above, ∆ABD ≅ ∆CBD.............(By SSS congruence rule)

(iii) ∠ABD = ∠CBD..................(Corresponding parts of congruent triangles)
So, BD bisects ∠ABC.