* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Section 2-8 - winegardnermathclass
Survey
Document related concepts
Steinitz's theorem wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Integer triangle wikipedia , lookup
Atiyah–Singer index theorem wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Noether's theorem wikipedia , lookup
Riemann–Roch theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
Section 2-8 Pages 124-131 Proving Angle Relationships After today’s lesson you should be able to: - Write proofs involving supplementary and complementary angles. - Write proofs involving congruent and right angles. Review: Supplementary angles add up to 180. Complementary angles add up to 90. Congruent angles have the same measure. Vertical angles are congruent. New Postulates and Theorems: Postulate 2.10 (Protractor Postulate) Given ray AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of ray AB, such that the measure of the angle formed is r. Postulate 2.11 (Angle Addition) If R is in the interior of LPQS, then mLPQR + mLRQS = mLPQS. If mLPQR + mLRQS = mLPQS, then R is in the interior of LPQS. Theorem 2.3 (Supplement Theorem) If two angles form a linear pair, then they are supplementary angles. Theorem 2.4 (Complement Theorem) If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles. Theorem 2.5: Congruence of angles is reflexive, symmetric, and transitive. Theorem 2.6: Angles supplementary to the same angle or to congruent angles are congruent. (L’s suppl. to same L or L’s are ) Theorem 2.7: Angles complementary to the same angle or to congruent angles are congruent. (L’s compl. to same L or L’s are ) Theorem 2.8 (Vertical Angles Theorem) If two angles are vertical angles, then they are congruent. Theorem 2.9: Perpendicular lines intersect to form four right angles. Theorem 2.10: All right angles are congruent. Theorem 2.11: Perpendicular lines form congruent adjacent angles. Theorem 2.12: If two angles are congruent and supplementary, then each angle is a right angle. Theorem 2.13: If two congruent angles form a linear pair, then they are right angles. Ex. 1: L6 and L8 are complementary, L8 = 47. 6 Ex. 2: 7 8 m(11) = x – 4, m(12) = 2x – 5. 11 12 W Ex. 3: Given: VX bisects LWVY VY bisects LXVZ Prove: LWVX LYVZ V X Z Statements Reasons Y