Proving Angle Relationships

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  • 0:01 Proving Angle Relationships
  • 0:27 Properties of Congruent Angles
  • 1:20 Supplementary and…
  • 2:22 Putting It All Together
  • 2:51 Lesson Summary
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Lesson Transcript
Instructor: Elizabeth Foster

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

In this lesson, you'll learn to prove angle relationships using properties of congruent, complementary, and supplementary angles. Learn the concepts and apply them on practice problems.

Proving Angle Relationships

Do proofs occasionally feel a little bit…complicated? In this lesson, we'll break it down and start with a few of the basic relationships. We'll start from the beginning with the properties of congruent angles. Understanding these rules can help you build a foundation for using more complicated theorems and properties. Then we'll kick it up a notch by adding complementary and supplementary angles to the mix.

Properties of Congruent Angles

Congruent angles are angles with the same measure. So for example, if you have two 62 degree angles, both are congruent.

Congruent angles have various properties that can help you do proofs with them:

  • The reflexive property states that an angle is congruent to itself. This one is confusing if you overthink it, but there's no secret meaning; there really is a rule in geometry literally saying that something is equal to itself.
  • The symmetric property states that if angle A equals angle B, then angle B equals angle A. It's called symmetric because the quantities on both sides of the equals sign are the same, so the equation is symmetrical. You can flip A and B from side to side, and it doesn't matter.
  • The transitive property states that if angle A equals angle B, and if angle B equals angle C, then angle A equals angle C.

Supplementary and Complementary Angles

Next up, some theorems about supplementary and complementary angles. Complementary angles add up to 90 degrees, or a right angle. Supplementary angles add up to 180 degrees, which is a straight line.

The complement theorem states that angles complementary to the same angle are congruent to each other. In this drawing (see video), angle A and angle B are both complementary to 64 degrees. So both angle A and angle B must be equal to 26 degrees. From this, we can say that angle A and angle B are equal to each other. This works even if we don't know what the values of any of the angles are. Even if we don't know what x is, we know that both A and B are equal to 90 - x, so they must be equal to each other.

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