What does SSS mean in math

Congruence theorem SSS, SWS, WSW and SSW

What is meant by congruence or congruence sentences is simply explained here. The drawing of triangles with a congruence sentence, however, can be found under Draw a triangle. Let's look at this:

  • A Explanation what congruence and the sentences to it are.
  • Examples for the congruence clauses SSS, SWS, WSW and SSW.
  • Tasks / exercises so that you can practice this yourself.
  • A Video to this topic
  • A Question and answer area to this area.

Tip: If you want to learn to draw triangles with the congruence clauses, you will find explanations and examples under Constructing triangles (drawing).

Explanation of congruence theorems

What is congruence anyway and what do you do with it?


Two triangles are congruent if they are congruent. You can move from one triangle to another by rotating, moving or mirroring. The rules for congruence are summarized with four congruence sentences.

Example congruence:

The two following triangles are congruent to each other, because you can get from one triangle to the other by moving and rotating.

Let's take a look at the four congruence theorems with example.

Congruence theorem SSS with example:

Let's start with the congruence theorem SSS. This says that if all three sides of the triangles match, they are congruent. Example: We have a triangle with the length of all three sides known. We simply rotate and move this and get two triangles that are congruent to each other.


Examples of congruence sentences

In this section we look at three more congruence theorems with examples.

Congruence sentence SWS with example:

Next, let's look at the SWS congruence theorem. This is about the fact that two sides and the included angle match. The next graphic shows two incomplete triangles.

If this is the case and you have finished drawing the triangles, they are also congruent to one another. The reason for this is that the three sides are the same length for both triangles and all angles are also correspondingly the same size.

Congruence theorem WSW with example:

The third case is the congruence theorem WSW. Two angles and the included side must match. The next graphic shows two incomplete triangles again. One side is given here and two angles are indicated.

If you finish drawing the triangles, you also get two triangles that are congruent to each other. These are shifted compared to the previous graphic so that the picture does not get too big.

Congruence theorem SSW with example:

The last congruence theorem is SSW. Here two triangles are congruent to each other if two sides and the angle opposite the longer side match. The next graphic shows a long side in red and a shorter side in blue. In addition, an angle is known which is opposite the longest side (red).

If you finish drawing the triangles, you also get two triangles that are congruent to each other.

Tasks / exercises congruence theorems


Videos of Congruence Theorems

Video SWW

This video uses an example to explain how a triangle is constructed according to SWW:

  • The video shows the approach to constructing a triangle with the information available.
  • It starts by constructing the given page as a horizontal line. The given angle is applied to this.
  • The finished triangle is created through parallel displacement and angular construction.

As a tool for this video, we recommend a set square, a pair of compasses, a sharp pencil and squared paper. Video source: Youtube.com

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Questions with answers congruence sentences

In this section, we'll look at questions with answers about the congruence sets.

Q: Does the WWW congruence theorem exist?

On a. There is no congruence for three angles. The reason for this is that the triangles can have a different size despite three equally large angles.

Q: Can I also draw triangles with the congruence sets?

A: You can learn how to do this under Constructing (drawing) a triangle.

Q: What topics should I look at next?

A: The congruence theorems are part of the geometry. In this area we have other content available, such as this one: