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# 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.
• 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.
• Are the postulates only AAS, ASA, SAS and SSS? Are there more postulates?
• RHS is also another postulate
RHS - Right angle Hypotenuse Side
• Is there some trick to remember all the different postulates?? There are so many and I'm having a mental breakdown. :'(
• When I learned these, our math class just did many problems and examples of each of the postulates and that ingrained it into my head in just one or two days. This may sound cliche, but practice and you'll get it and remember them all.
• In AAA why is one triangle not congruent to the other?
• You can have triangle of with equal angles have entire different side lengths. For example Triangle ABC and Triangle DEF have angles 30, 60, 90. However, the side for Triangle ABC are 3-4-5 and the side for Triangle DEF are 6-8-10. Therefore they are not congruent because congruent triangle have equal sides and lengths.