Question

In the figure given below,AB=DC and AC=DB.Is ∆ABC =~∆DCB.
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Answer 1

Firstly let us know that what is Congruency,

Two figures are congruent if they have same shape and size and both the object concides with each other.

There are mainly four congruency criterions...

1. Side Side Side (SSS)

2. Side Angle Side (SAS)

3. Angle Side Angle (ASA)

4. Right Angle Hypotaneuse and One side (RHS)

In this question ,

Given that ,

AB = DC

AC = DB

Let us see ,

In △ABC and △DCB ,

AB = DC (given)

AC = DB (given)

BC = BC (common side)

∴YES , △ABC ≅ △DCB

(By SSS criteria)..

Answer 2

First of all let us try to understand what is congruence ?
If you draw two circles of the same radius and cut them and then place one on other, what do you observe ?
They cover Each Other completely and such figures are called congruent figures. "Congruent" means equal in all respects or figures whose shapes and sizes are both the same.

So, now coming to the question it is stated that :-
• AB = DC
• AC = DB

To Find

∆ ABC ≈ ∆ DCB

Solution :-

We know that

AB = DC
AC = DB
BC = BC ( As BC is common in both the triangles )

So, we can conclude that both the triangles are congruent by Side-Side-Side congruence conditions as two of the sides are equal and the third one is common.

Hence, ∆ ABC ≈ ∆ DCB


There are three more congruence conditions, they are :-

• SAS : Side-Angle-Side
• ASA : Angle-Side-Angle
• RHS : Right Angle-Hypotenuse-Side