Congruence in geometry refers to two figures that have the exact same shape and size, meaning they can perfectly overlap when placed on top of one another.

There are 4 criteria to determine that two triangles are congruent.In this article, we will learn to use the third criterion of congruence:

Side, Side, Side (SSS)

Definition:

2 triangles in which their three sides are of the same length are congruent triangles.

Recognizing Congruent Sides:

To determine if two triangles are congruent using the Side-Side-Side (SSS) criterion, compare the lengths of their sides. If all three corresponding sides in both triangles are equal, the triangles are congruent. This means they will have identical shapes and sizes, even if their orientations differ.

Flipped Triangles:

It’s important to note that congruent triangles may appear flipped or rotated. As long as the corresponding sides match, the triangles are still congruent. You can check this by mentally or physically rotating or flipping one triangle to align with the other.

What is the congruence criterion for two triangles?

There are four triangle congruence criteria, which allow us to determine if two triangles have the same lengths in their sides and likewise the same degrees in their corresponding angles. In this way, we can say that the two triangles, even when they are in different positions or orientations, will have the same shape and size.

What is the SSS congruence criterion?

This criterion allows us to deduce if two triangles have the same shape and size. According to this criterion, two triangles are congruent when their three sides are equal.

What is the difference between the SSS congruence criterion and the SSS similarity criterion?

The SSS congruence criterion tells us that if two triangles have their three sides equal (congruent sides), then the two triangles are identical, meaning they have the same measurements in terms of sides and angles. Whereas the SSS similarity criterion tells us that if two triangles are similar, then their three sides are proportional, meaning they do not have the same measurement but they do have some proportion between them and they have the same shape, but with different measurements in terms of their sides.

Which pair of triangles are similar by the SSS criterion?

Two triangles will be similar when they have the same shape, regardless of orientation, that is, their corresponding angles are equal but their corresponding sides do not necessarily have the same length, instead, they must have a proportion between them.

What are the criteria for similarity and congruence of triangles?

Congruence criteria

The four triangle congruence criteria are:

SAS - Side, Angle, Side.

ASA - Angle, Side, Angle.

SSS - Side, Side, Side.

SSA - Side, Side, Angle.

Similarity criteria

Unlike the congruence criteria, there are only three triangle similarity criteria:

SSS - Side, Side, Side.

SAS - Side, Angle, Side.

AAA - Angle, Angle, Angle.

Test your knowledge

Question 1

EC = EB

AC = AB

According to which congruence theorem is ΔECA ≅ ΔEBA?