Question

In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see Fig. 7.16). Show that ∆ ABC ≅ ∆ ABD. What can you say about BC and BD?

Answer 1

In ∆ABC and ∆ABD, 

AC = AD (Given) 

∠CAB = DAB (AB bisects ∠A) 

AB = AB (Common) 

∴ ∆ABC≅ ∆ABD (By SAS congruence rule) 

∴ BC = BD (By CPCT) 

Therefore, BC and BD are of equal lengths.