Geometry Notes Sections 2-8 What you’ll learn How to write proofs involving supplementary and complementary angles How to write proofs involving congruent and right angles Vocabulary There is no new vocabulary However. . . Do you know these definitions. . .? Supplementary Angles Adjacent Angles Complementary Angles Congruent Segments Reflexive Property Angle Addition Postulate Symmetric Property Segment Addition Postulate Transitive Property Midpoint Perpendicular lines Segment Bisector Linear Pair of Angles Angle Bisector Vertical Angles Opposite Rays Congruent Angles I hope so. . . . Congruence of Segments is . . . Reflexive segments Symmetric segments Transitive segments A segment is congruent to itself. AB AB You can switch the left and right sides If AB CD then CD AB. If AB CD and CD EF, then AB EF. Congruence of Angles is . . . Reflexive angles An angle is congruent to itself. A A You can switch the left and right sides Symmetric angles If A B then B A. Transitive angles If A B and B C, then A C. Supplement Theorem If two angles form a linear pair, 2 1 then they are supplementary supplementary. What are we given? Look in the hypothesis of the conditional statement and draw it. Now what can we conclude? Look in the conclusion of the conditional statement 1 and 2 are supplementary. How does this work in problems? If 1 and 2 form a linear pair and m2 = 67, find m1. 1 2 Linear pairs → supplementary → add up to 180 More example problems Find the measure of each angle. Linear pairs → supplementary → add up to 180 More example problems Find the measure of each angle. Linear pairs → supplementary → add up to 180 Vertical Angles We’ve done this before. Draw two vertical angles If two angles are vertical angles then they are congruent. Vert. s → → = How does this work in problems? If m2 = 72, find m1. Vert. s → → = 1 2 More example problems Find the measure of each angle. Vert. s → → = More theorems. . . Complement theorem If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles. 2 1 1 & 2 complementary → m 1 + m 2 = 90 More theorems. . . Angles supplementary to the same angle or to two congruent angles are congruent. More theorems. . . Angles complementary to the same angle or to two congruent angles are congruent. More theorems. . . Perpendicular lines intersect to form four right angles. All right angles are congruent. Perpendicular lines form congruent adjacent angles. If two angles are congruent and supplementary, then each angle is a right angle. If two congruent angles form a linear pair, then they are right angles. Have you learned .. . . How to write proofs involving supplementary and complementary angles? How to write proofs involving congruent and right angles? Assignment: Worksheet 2.8A