**triangles are congruent only when all interior angles and congruent sides of the triangle are congruent**. If we want to determine that which two triangles are congruent to each other then we have to search ,that any of these conditions are satisfied or not. So the conditions are as follows:

To understand we assume that we have two triangles $\Delta$ABC and $\Delta$A'B'C' in which $\Delta$ABC contains three sides a, b, c respectively and triangle $\Delta$A'B'C' contains three sides a’, b’ and c' respectively. So according to first condition if two pairs of sides of both triangles and one angle of both triangles is same then we can say that triangles are congruent. So we can write that

b = b’, c = c' and $\angle$A = $\angle$A then triangles $\Delta$ABC and $\Delta$A'B'C' are congruent.

If in case that if two triangles $\Delta$ABC and $\Delta$A'B'C' have two pair of angles are same with one side is common in both then the triangles are said to be congruent.

$\angle$A = $\angle$A’, $\angle$B = $\angle$B' and c = c' then triangles $\Delta$ABC and $\Delta$A'B'C' are congruent.

If all sides of triangle $\Delta$ABC and triangle $\Delta$A'B'C' are same then we can say that triangles are congruent. So we can write that

a = a’, b = b’, c = c',

To understand congruence triangles more deeply we take an example where we have two triangles DEF and $\Delta$D’E’F’. Now we have to find that both triangles are Geometry congruent triangles or not. The sides of $\Delta$DEF are d = 1 , e = 2 and f = 3. The triangle $\Delta$D'E'F' sides are d' = 1, e' = 2 and f' = 3. Now we have to find out that both triangles are congruent or not.

Here we can easily see that sides of both triangles are same so

d = d' = 1, e = e' = 2, f = f' = 3

Both triangles are congruent triangle.