Question

In Fig 7.13, AD = CD and AB = CB. Is ΔABD ≅ ΔCBD? Why or why not?

Answer 1

Answer:

ΔABD ≅ ΔCBD

Step-by-step explanation:

As given in question,

AD=CD,

AB=CB,

Now,as shown in fig,

Side BD is common to both the triangle

so,ΔABD ≅ ΔCBD (by SSS congruency )

Answer 2

It is true that ΔABD ≅ ΔCBD.

• In ΔABD and ΔCBD, it is given that AD = CD , AB = CB.
• Now we have to prove that the triangles ΔABD and ΔCBD are congruent.
• We have various test to prove the congruence of triangles.

We start by given,

In ΔABD and ΔCBD,

AB = CB  (Given)

BD = BD   (Common side)

AD = CD   (Given)

• Therefore the above given triangles are congruent.

ΔABD ≅ ΔCBD   (By SSS test of congruence)

• The two triangles are congruent as the corresponding sides of the two triangle are congruent.