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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.

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• For the second problem, couldn't you just have used the alt. int. angles theorem converse?
• I think so. As long as it makes sense and you get the desired conclusion, your proof is correct
• 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 just ways to identify similar or congruent triangles. The S stands for corresponding sides of equal measure on each triangle, and the A stands for corresponding angles of equal measure on each triangle. So for SSS, all three sides of a triangle would have the same lengths of all of the sides of another triangle. For AAA (or just AA, because you only need two of the angles) it would be the same thing, all three angles of a triangle would be the same as the angles on another triangle. However, because no sides must be related in this case, you are only getting similar triangles, not congruent ones. For ASA and SAS, two angles (ASA) or two sides (SAS) and the angle (for SAS) or a side (for ASA) that is surrounded by the two sides/angles; if these measures are equal to measures in the same position of another triangle, then they are congruent (an example of ASA would be at ). ASS and SSA don't actually work, but AAS and SAA work. For those comparisons, if two angles and a side that is not between them have the same measure as another triangle's two angles and an outside side, then both of those are congruent. It is really difficult to explain it without having any visuals, but I would have thought that the KA videos would have explained it well enough, but I haven't seen them, so I don't know.
• Isn't the second theorem just a converse of the first theorem ?
• It is just a converse of the first theorem.
• When labeling that the triangles are congruent by the ASA theorem. How do you identify the corresponding parts and then label?
• Pretend a triangle is ABC and XYZ. If you right that it means angle A = angle X, B = Y, C = Z, line AB = line XY, BC = YZ, and AC = XZ.
• how can we say that angle abd=bdc in the first instance?
• We can say that abd=bdc because the line he drew through the parallelogram is technically a transversal. Because it is a transversal, the two angles it forms are congruent, since we already know that the lines are parallel to each other. Hope this helps :)
• Alternate interior angles at :: What are they?
• 'When two lines are crossed by another line (which is called the Transversal), the pairs of angles
• on opposite sides of the transversal
• but inside the two lines
are called Alternate Interior Angles.' Reference: www.mathsisfun.com
• What does the equal sign with the ~ mark on top mean?
• It is the congruent sign. It means that two shapes are congruent.
• 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.
• Could you give a easy-to-understand explanation of the 'if and only if' logic used in math? (like in the example at )
Any help would really be appreciated!
• Lets talk about a square.
If it is a square, then it is a quadrilateral with all right angles and congruent sides.
If a quadrilateral has all right angles and congruent sides, then it is a square.
So both the original statement and its converse (switching the hypothesis and conclusion) are both true. Thus, we can combine it into an if and only if statement, It is a square if and only if it is a quadrilateral with all right angles and congruent sides.
It does not work if the converse is not true such as if you live in Houston, then you live in Texas. The converse is If you live in Texas, then you live in Houston which is false, there a number of counterexamples such as Dallas, Austin, etc.