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# Proof: Opposite sides of a parallelogram

Sal proves that a figure is a parallelogram if and only if opposite sides are congruent. Created by Sal Khan.

## Want to join the conversation?

• Is AAA and AAS is appropraite property for prooving that the triangles are congruent?
• You need at least one side, so AAS is okay but AAA is not. AAA can be any size.
• My suggestion to you is to watch the video, do some practice questions, and then if you don't understand try searching it up on YouTube. So you can get other people's points of view.
• Isn't the second theorem just a converse of the first theorem ?
• Yep. That is correct because the converse is only in the first theorem or proof because they move on to different stuff after it is solved.
• I still dont quite grasp the side angle thing (SSS AAA SAS ASA ASS SSA) I watched the vids explainin them a lot and still dont get it and I c thatthey keep poppin up on the other geometry vids!!! HELP?!!!?!
• they are all just ways to show whether or not triangles are congruent. the "S" stands for "side" and "A" stands for "angle". The congruence theorem of "ASS" does not work and I'll explain it in an interesting story. Back in the old days when they were driving herds of horses and donkeys(asses), whenever they got to a bridge the horses would cross just fine but the donkeys were afraid to cross. In Euclid's proposition 5 the diagram takes the shape of a bridge and mathematicians over time called it the "Pons Asinorum" or the "bridge of asses". This was part of proving a congruence theorem and it was said that if asses could learn geometry then they would get no further than prop 5. It also shows that "angle , side ,side " congruence does not work which means "ASS" can't cross the bridge.
• What do you call it when a line like DB is congruent to itself? Reflexiv? Reflexiv property? Reflexive postulate? Sal mentioned it briefly in one of the videos on triangles I think but I can't find it.
• for the second problem could you use a theroum
• congruent means equal or same as . Right?
• Yes. Specifically, we say two geometric figures are 'congruent' if you can pick up one and place it perfectly over the other without distorting them.