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## High school geometry

### Course: High school geometry>Unit 3

Lesson 2: Triangle congruence from transformations

# Proving the SSS triangle congruence criterion using transformations

We can prove the side-side-side (SSS) triangle congruence criterion using the rigid transformation definition of congruence. Created by Sal Khan.

## Want to join the conversation?

• I think there is a mistake at .Should Sal have put 4 hash marks on that line? Thanks • What is even triangle congruence criterion? Before we try to prove it. Did i miss something along the way? • A Triangle Congruence Criterion is a way of proving that two triangles are congruent. There are four types of criterians. There is SSS (Side, Side, Side). This means if each of the 3 sides of one of the triangles are equivalent to the other 3 sides on the other one, then they are both congruent. Another example is SAS (Side, Angle, Side). This means that if one angle (it has to be shared by the two other sides, I’ll explain what this means) is equal on both triangles, and two sides on that angle are equal on both triangles, it proves that they are congruent. You might be thinking, why can’t I rearrange the letters in the criterion? Well, we can rearrange SAS into SSA. But Sal shows in one of his videos that SSA is not a criterion that shows that two triangles are congruent. But, there is ASA and AAS. The difference between these two, is that in ASA, one of the sides in a triangle has to be shared by two angles. In simple terms, two angles have to be shown on that same side. So in SAS and ASA, if A or S is in the middle of two same letters, then that angle or side has to have two sides on the same angle (for SAS) and for ASA, one side has to show two angles on it. If you are confused, which is most probably true, then you can ask me questions on this same comment you posted.
• At , what does Sal mean when he said "compass?" Did he mean the compass we use in science? • The tool in Sal's hand is called a compass, and it's different from a directional compass you would use to navigate.

Given two points on our paper, we use a compass to draw a very accurate circle centered on one point, and with its circumference passing through the other point.

Along with a compass, you usually also have a straightedge, which is a ruler with no markings on it. With these two tools, you can play a sort of game by making challenges. Using only compass and straightedge, can you make an equilateral triangle? Given an angle, can you use a compass and straightedge to bisect it perfectly? Draw a regular pentagon? Construct an angle of exactly 20º? And so on.
• Howdy! I have a big problem. The videos that I am supposed to be watching don't have anything to do with the questions. For example, he is talking about the congruence criterion in all of the videos, however, the questions don't really address that. They ask me three questions, to justify the steps above, whether they are at the same distance from DE or whether they are on the same ray and the like, did you put the wrong questions, or am I just not understanding them? HELP PLEASE • I understand what he is saying, but none of those relate to the practice questions. Can someone help me with the practice problems? • How did he demonstrate that point E and D must sit on the perpendicular bisector of line FC? I think I am missing some logic. Somebody please help me with this. • I don't understand the perpendicular bisector scene!
What is a perpendicular bisector? • What exactly is SSS? • Let’s say that we have two triangles, triangle A and triangle A’. SSS (Side-Side-Side) is a theorem that says that if all the sides of A is equal to all the sides of A’, triangles A and A’ are congruent. In other words, SSS states that if the measure three sides of one triangle are equal to the measure of three sides of another triangle, the two triangles are congruent.  