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### Course: Geometry (FL B.E.S.T.)>Unit 5

Lesson 5: Theorems concerning quadrilateral properties

# 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?

• 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.
• 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 :)
• 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.
• What does the equal sign with the ~ mark on top mean?
• It is the congruent sign. It means that two shapes are congruent.
• 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
• For the first problem couldn't you have just drawn the diagonal and found they were congruent by the SSS postulate?
• The SSS postulate says 'if two traingles have all three pairs of sides congruent, then the triangles are congruent.' From the given information in the first problem, we don't know that the triangles have three congruent side pairs, so we can't use that postulate.
• Is there a specific order to write the angles?
for example: ADB is congruent to CBD
• Ok!
When naming angles, remember:

The order of letters matters and indicates the direction you're moving around the vertex.
For instance, "ADB" refers to the angle at point D with rays extending to points A and B, while "CBD" refers to the angle at point D with rays extending to points C and B.

So, "ADB is congruent to CBD" means that the angle formed at point D with rays extending to points A and B is equal in measure to the angle formed at point D with rays extending to points C and B.