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# Determining congruent triangles

Sal uses the SSS, ASA, SAS, and AAS postulates to find congruent triangles. Created by Sal Khan.

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• How would triangles be congruent if you need to flip them around?
• Congruent means the same size and shape. It doesn't matter if they are mirror images of each other or turned around. If you could cut them out and put them on top of each other to show that they are the same size and shape, they are considered congruent. Rotations and flips don't matter.
• in ABC the 60 degree angle looks like a 90 degree angle, very confusing.... :=D
• Math teachers love to be ambiguous with the drawing but strict with it's given measurements. Always be careful, work with what is given, and never assume anything.
• how are ABC and MNO equal? both of their 60 degrees are in different places
• Basically triangles are congruent when they have the same shape and size. So if you have two triangles and you can transform (for example by reflection) one of them into the other (while preserving the scale!), the two triangles are congruent.
If you flip/reflect MNO over NO it is the "same" as ABC, so these two triangles are congruent.
• Can you expand on what you mean by "flip it". I cut a piece of paper diagonally, marked the same angles as above, and it doesn't matter if I flip it, rotate it, or move it, I cant get the piece of paper to take on the same position as DEF.
• The triangles that Sal is drawing are not to scale.
• does it matter if a triangle is congruent by any of SSS,AAS,ASA,SAS?
• Your question should be about two triangles. This is because by those shortcuts (SSS, AAS, ASA, SAS) two triangles may be congruent to each other if and only if they hold those properties true.
SSS: When all three sides are equal to each other on both triangles, the triangle is congruent
AAS: If two angles and a non-included (you can think of it as outside) side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
ASA: If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
SAS: If any two angles and the included side are the same in both triangles, then the triangles are congruent.
• Is there a way that you can turn on subtitles?
• Yeah. There's this little button on the bottom of a video that says CC. That will turn on subtitles. Different languages may vary in the settings button as well. If you hover over a button it might tell you what it is too.
• why doesn't this dang thing ever mark it as done
• IDK. It happens to me though. When it does, I restart the video and wait for it to play about 5 seconds of the video. Then I pause it, drag the red dot to the beginning of the video, push play, and let the video finish. For some unknown reason, that usually marks it as done. I hope it works as well for you as it does for me.
• Why are AAA triangles not a thing but SSS are? If you can't determine the size with AAA, then how can you determine the angles in SSS?
• Two triangles that share the same AAA postulate would be similar. But if all we know is the angles then we could just dilate (scale) the triangle which wouldn't change the angles between sides at all.

If we know that 2 triangles share the SSS postulate, then they are congruent. This means that they can be mapped onto each other using rigid transformations (translating, rotating, reflecting, not dilating).

There is only 1 such possible triangle with side lengths of A, B, and C. Note that that such triangle can be oriented differently, using rigid transformations, but it will 'always be the same triangle' in a manner of speaking.

Angles tell us the relationships between the opposite/adjacent side(s), which is what sine, cosine, and tangent are used for.

Hope this helps!
- Convenient Colleague