Question

In the given figure, 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.