Which of the following statements is sufficient to conclude that two triangles are congruent?

Correct option is A

Concept Used:

For two triangles to be congruent their corresponding sides and corresponding angles are equal

Solution:

We know 4 conditions to prove that triangles are congruent which are SSS ,SAS ,ASA and RHS 

Checking the conditions:

1)If two triangles have same base and height

We cannot tell if triangle are congruent as two triangle can have same base and height but different sides.

We can only tell that these two have same area.

2)If one side and one angle are same 

For congruency we need at least two sides and one angle ( SAS) or two angles and one side (ASA)

3)If they have same area and base

Still here have only one side so we cannot tell about congruency

4)If they have two same sides and same perimeter.

If  two sides are equal and perimeter is also equal then third will also be equal

So if all sides are equal we can say trianlges are congruent (SSS congruency)