* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PP Prove Angle Pair Relationships Lesson 4.6 for 1-18
Survey
Document related concepts
Line (geometry) wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Steinitz's theorem wikipedia , lookup
Integer triangle wikipedia , lookup
Atiyah–Singer index theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Riemann–Roch theorem wikipedia , lookup
Noether's theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
Prove Angle Pair Relationships Lesson 4.6 Page 223 Lesson 4.6 The goal of this lesson is to be able to use the properties of special pairs of angles. Adjacent Angles 1. Two angles that share a common vertex and side, but have no common interior points are called adjacent angles. C D A B ABC is adjacent to CBD. Linear Pair 2. Two adjacent angles are a linear pair if their noncommon sides are opposite rays. C ABC + CBD = 180 A D B Theorem 4.3 3. Right Angles Congruence Theorem: All right angles are congruent. C A B m ABC = 90 Theorem 4.4 4. Congruent Supplements If m1 + m2 = 180 Theorem: If two angles are and m1 + m3 = 180 supplementary to the same angle (or to then m2 = m3. congruent angles), then they 2 3. are congruent. Theorem 4.5 5. Congruent Complements Theorem: If m1 + m2 = 90 If two angles are complementary to the and m1 + m3 = 90 same angle (or to then m2 = m3. congruent angles), then they are congruent. 2 3. Linear Pair Postulate: 6. If two angles form a linear pair, then they are supplementary. 1 2 m1 + m2 = 180 Theorem 4.6 7. Vertical Angles Congruence Theorem: If m1 + m2 = 180 Vertical angles are and m1 + m3 = 180 congruent. then m2 = m3. 1 2 3 2 3. Example 1 Guided Practice Example 2 Example 3 Homework Assignment: Page 225 # 1 – 14 all