Question

In quadrilateral ACBD, AC = AD and AB bisects ∠A. Show that ΔABC ≌ ΔABD. What can you say about BC and BD?

Answer 1

Explanation:

Ans. In quadrilateral ABCD we have                  

AC = AD          

and

AB being the bisector of ∠A.            

Now, in ΔABC and ΔABD,                  

AC = AD[Given]                  

AB = AB[Common]

∠CAB = ∠DAB [∴ AB bisects ∠CAD]          

∴ Using SAS criteria, we have                  

ΔABC ≌ ΔABD.            

∴ Corresponding parts of congruent triangles (c.p.c.t) are equal.          

∴ BC = BD.