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## Geometry (FL B.E.S.T.)

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

Lesson 5: Theorems concerning quadrilateral properties

# Proof: Opposite angles of a parallelogram

Sal proves that opposite angles of a parallelogram are congruent. Created by Sal Khan.

## Want to join the conversation?

• When comparing angles of equal measure in this video Sal uses a congruent symbol. Would it be equally acceptable to use a plain equals sign instead?
If not, when would you use a congruent symbol and when would you use an equals sign to compare angles?
• No, it would not. If you were talking specifically about the measures of the angles, then you could, but when referring to the angle itself, you should use the congruence symbol.
• Is point D a right angle at ?
• Technically, point D is not an angle :)

Since Sal is talking about parallelograms, the angle BDC (the angle defined by the line segments BD and CD) isn't necessarily a right angle, but it's not impossible for it to be a right angle.

You can't assume that BDC is a right angle, because if you did, you'd only prove that the opposite angles of a parallelogram are equal if one of the angles is a right angle (from which would follow that the other three angles are right angles too).

When proving things, you want to make as little assumptions as possible so that your proof applies to as many scenarios as possible.
• Math really is another language. And I am not fluent.

How does one name angles? It seems like it's random mostly, but I'm not sure.

Just wondering. :D
• In all reality, you can name an angle anything, as long as it is a variable. But sometimes people name them as numbers, but the y have to be in order and they all have to in numbers. Hope this helped.
• Aren't opposite angles of a parallelogram corresponding angles or alternate interior angles?
• No they are not corresponding or alternate interior angles. They are just called opposite angles and they are equal to each other.
• If 𝐴𝐵𝐶𝐷 is a trapezoid, where side 𝐴𝐵 is parallel to side 𝐶𝐷,
then angles 𝐴 and 𝐷 are supplementary, as are angles 𝐵 and 𝐶.
• why is the ~ place top on the =?
• That means that the two figures are congruent. Just ~ means similar. Hope I helped!
• What is the difference between Congruence and Equivalence?
• `The fact is that they are not the same. Congruence is a relationship of shapes and sizes, such as segments, triangles, and geometrical figures, while equality is a relationship of sizes, such as lengths, widths, and heights. Congruence deals with objects while equality deals with numbers.`
• define congruent, does it mean equal
(1 vote)
• In geometry two shapes are congruent if they have the same shape or size. So yes, congruent means "Equal in size or shape."