If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Geometry (FL B.E.S.T.)>Unit 4

Lesson 3: Congruent triangles

# Triangle congruence postulates/criteria

Sal introduces and justifies the SSS, SAS, ASA and AAS postulates for congruent triangles. He also shows that AAA is only good for similarity. For SSA, better to watch next video. Created by Sal Khan.

## Want to join the conversation?

• So when we talk about postulates and axioms, these are like universal agreements? No one has and ever will be able to prove them but as long as we all agree to the same idea then we can work with it. Am I right in saying that? Similar to BIDMAS; the world agrees to perform calculations in that order however it can't be proven that it's 'right' because there's nothing to compare it to.
• Nice analogy! They are a starting point.
If you agree with rule X, then I can prove Y.
• I think Sal said opposite to what he was thinking here. He said "we are not constraining the angle, but we are constraining the length of that side".

Correct me if I'm wrong, but not constraining a length means allowing it to be longer than it is in that first triangle, right? But he can't allow that length to be longer than the corresponding length in the first triangle in order for that segment to stay the same length or to stay congruent with that other segment in the other triangle.

So he has to constrain that length for the segment to stay congruent, right? Meaning it has to be the same length as the corresponding length in the first triangle?

So he must have meant not constraining the angle! Not the length of that corresponding side.

Also at he implied that the yellow angle in the second triangle is the same as the angle in the first triangle. But that can't be true? is it?...

I mean if you are changing one angle in a triangle, then you are at the same time changing at least one other angle in that same triangle. If that angle on top is closing in then that angle at the bottom right should be opening up. Ain't that right?...

So what happens then? It still forms a triangle but it changes shape to what looks like a right angle triangle with the bottom right angle being 90 degrees? I essentially imagine the first triangle and as if that purple segment pivots along a hinge or the vertex at the top of that blue segment.
• So, is AAA only used to see whether the angles are SIMILAR?
• yep. It cannot be used for congruence because as long as the angles stays the same, you can extend the side length as much as you want, therefore making infinite amount of similar but not congruent triangles
• in my geometry class i learned that AAA is congruent. why isn't it?
• It is similar, NOT congruent. The lengths of one triangle can be any multiple of the lengths of the other. For example, all equilateral triangles share AAA, but one equilateral triangle might be microscopic and the other be larger than a galaxy.
• SSS - Side Side Angle
SAS - Side Angle Side
ASA - Angle Side Angle
AAS - Angle Angle Side
AAA - Angle Angle Angle
SSA - Side Side Angle
RSH - Right angle Side Hypotenuse
Postulate - Suggest or assume the existence of something as a basis for reasoning.
• Note that SSA and AAA cannot be used to prove the congruence of two triangles, but AAA can be used with spherical geometry. SSS means side side side, by the way. sorry for the mistake.
• Does anybody know why these congruence postulates are limited to 3 letter? I mean, won't SASASA ensure that the given figures are congruent?
• This is the beauty of triangle congruence postulates. Often, we just need three congruences (with the exception of SSA and AAA) to prove that triangles are congruent, so we get six congruences for the price of three!

Have a blessed, wonderful day!
• why am i studying proofs if i dont even need them in the real world
• You would need this in all sorts of engineering and manual labor.
Hope this helps!
• for SSA i think there is a little mistake. If you notice, the second triangle drawn has almost a right angle, while the other has more of an acute one. I may be wrong but I think SSA does prove congruency. So could you please explain your reasoning a little more. Thanks
• Well Sal explains it in another video called "More on why SSA is not a postulate" so you may want to watch that.