1 / 12

2-5 Proving angles congruent

2-5 Proving angles congruent. Vertical angles. Two angles whose sides are opposite rays. 1. 4. 3. 2. Adjacent angles. Two coplanar angles with a common side , a common vertex , and no common interior points. 3. 4. 1. 2. Complementary angles. Two angles that ADD up to 90˚

issac
Download Presentation

2-5 Proving angles congruent

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2-5 Proving angles congruent

  2. Vertical angles • Two angles whose sides are opposite rays 1 4 3 2

  3. Adjacent angles • Two coplanar angles with a common side, a common vertex, and no common interior points 3 4 1 2

  4. Complementary angles • Two angles that ADD up to 90˚ • Each angle is called the complement of the other 50° 1 A 2 40° B

  5. Supplementary Angles • Two angles that ADD up to 180° • Each angle is called the supplement of the other 105° 75° 3 4

  6. Examples! • 1. Identify Angle Pairs • Complementary • Supplementary • Vertical • Adjacent 2 1 3 5 4

  7. 2. What can you tell from the picture? • About ∠1 and ∠2? • What type of angles are ∠2 and ∠3? • What type of angles are ∠4 and ∠5? • What type of angles are ∠1 and ∠4? 3 2 4 1 5

  8. Vertical Angles Theorem (2-1) • Vertical angles are congruent (≅) • ∠1 ≅ ∠2 and ∠3 ≅ ∠4 1 4 3 2

  9. Using the vertical angles theorem • Find the value of x. • Find the value of each angle. 4x (3x + 35)

  10. Congruent Supplements Theorem (2-2) • If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. • ∠1 and ∠2 are supplementary (∠2 is a supplement of ∠1) • ∠1 and ∠3 are supplementary (∠3 is a supplement of ∠1) • So ∠2 ≅ ∠3 2 3 1

  11. Congruent Complements Theorem (2-3) • If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. • Theorem 2-4: All right angles are congruent. • Theorem 2-5: If two angles are congruent and supplementary, then each is a right angle.

  12. Ticket Out the door

More Related