CHAPTER 2: DEDUCTIVE REASONING Section 2-4 A: Special Pairs of Angles.

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Presentation transcript:

CHAPTER 2: DEDUCTIVE REASONING Section 2-4 A: Special Pairs of Angles

ADJACENT ANGLES Recall Adjacent Angles: 2 angles with a common vertex and a common side, but no common interior points. 1 and 2 are adjacent 1 2

LINEAR PAIR Recall Linear Pair: 2 adjacent angles whose non- common sides form a line (a straight angle). 1 and 2 are a linear pair. Straight Angle: a straight angle measures

SUPPLEMENTARY ANGLES Supplementary Angles: 2 angles whose measures add to 180. AdjacentNon-adjacent Suppl. angles suppl. angles

LINEAR PAIR THEOREM Linear Pair Theorem: If 2 angles form a linear pair, then they are supplementary.

LINEAR PAIR THEOREM: Given: 1 and 2 are a linear pair Prove: 1 and 2 are supplementary 1. 1 and 2 are a linear pair 2. ABC is a straight 3.m ABC = m 1 + m 2 = m ABC 5.m 1 + m 2 = and 2 are supplementary 1.Given 2.Definition of a linear pair 3.Definition of a straight 4.Angle add. Postulate 5.Substitution 6.Definition of supplementary angles 12 D ABC

EXAMPLES 1.Find x. 2x x = 180 5x + 30 = 180 5x = 150 x = 30 3x2x + 30

EXAMPLES 2. A and B are supplementary. m A = x m B = 2x – 50. Find x, m A, and m B x x – 50 = 180x + 202x x – 30 = (70) x = 210 m A = x = 70 m B = 90

EXAMPLES 3. D and E are supplementary. E is 5 times as large as D. Find the measure of each angle. Let m D = x. Thus, m E = 5x. If m D + m E = 180, then x + 5x = 180. x + 5x = 1805x 6x = 1805 (30) x = 30 so m D = 30m E = 150

COMPLEMENTARY ANGLES Complementary Angles: 2 angles whose measures add to 90. Non-adjacent complementary Adjacent complementary angles since = 90angles. F G A B C 1 2

EXAMPLES 4.Find x. 5x – x = 90 9x – 45 = 90 9x = 135 x = 15 5x x

EXAMPLES 5.C and D are complementary. m C = x + 50 and m D = 3x – 20. Find x, m C, and m D. x x – 20 = 90 4x + 30 = 90 4x = 60 x = 15 m C = x + 50m D = 3x - 20 = = 3(15) - 20 = 65= 45 – 20 = 25

EXAMPLES 6.H and J are complementary. H is twice as large as J. Find the measure of each angle. H = 2x J = x x + 2x = 902x 3x = 902(30) x = 30m H = 60

CLASSWORK/HOMEWORK CW: Pg. 51, Classroom Exercises 1-9 all HW: Pg. 52, Written Exercises 1-10 all