LINES AND ANGLES 28 PARALLEL LINES Def line

LINES AND ANGLES

28 PARALLEL LINES • Def: line that do not intersect. B • Illustration: A l m • Notation: D C l || m AB || CD p. 129

Examples of Parallel Lines • • • Hardwood Floor Opposite sides of windows, desks, etc. Parking slots in parking lot Parallel Parking Streets: Laramie & Le. Claire

PERPENDICULAR LINES 29 • Def: Lines that intersect to form a right angle. m • Illustration: n • Notation: m n • Key Fact: 4 right angles are formed. p. 79

Ex. of Perpendicular Lines • Window panes • Streets: Belmont and Cicero

Transversal 30 • Def: a line that intersects two lines at different points t • Illustration: p. 131

Vertical Angles • Two angles that are only touching by a vertex and are congruent angles. t 1 2 3 4 5 7 6 8 1 4 2 3 5 8 6 7

Vertical Angles • Find the measures of the missing angles t 125 ? 125 55 ? 55

Supplementary Angles/ Linear Pair • Two angles that form a line (sum=180 ) 1+ 2=180 2+ 4=180 4+ 3=180 3+ 1=180 t 1 2 3 4 5 7 6 8 5+ 6=180 6+ 8=180 8+ 7=180 7+ 5=180

Supplementary Angles/ Linear Pair • Find the measures of the missing angles t 108? 72 108 ? 180 - 72

30 Corresponding Angles • Two angles that occupy corresponding positions. t Top Left Top Right 1 3 Bottom Left Top Left Bottom Left 2 5 7 4 Bottom Right 6 Top Right 1 5 2 6 3 7 4 8 8 Bottom Right p. 131 & 143

Corresponding Angles • Find the measures of the missing angles t 145 35 ? 145

Alternate Interior Angles 30 • Two angles that lie between parallel lines on opposite sides of the transversal t 1 2 3 4 3 6 4 5 5 6 7 8 p. 131 & 143

Alternate Interior Angles • Find the measures of the missing angles t 82 98 ? 82

Alternate Exterior Angles 30 • Two angles that lie outside parallel lines on opposite sides of the transversal t 1 2 3 4 2 7 1 8 5 6 7 8 p. 131 & 143

Alternate Exterior Angles • Find the measures of the missing angles t 120 60 ? 120

Consecutive Interior Angles 30 • Two angles that lie between parallel lines on the same sides of the transversal t 1 2 3 4 3 + 5 = 180 4 + 6 = 180 5 6 7 8 p. 131 & 143

Consecutive Interior Angles • Find the measures of the missing angles t 135 ? 45 180 - 135

Corresponding 4 and 2 3 and 1 5 and 7 6 and 8 5 4 6 3 7 2 1 8 t

Alternate Interior 3 and 7 2 and 6 5 4 6 3 7 2 1 8 t

Alternate Exterior 5 and 1 4 and 8 5 4 6 3 7 2 1 8 t

Consecutive Interior 3 and 2 6 and 7 5 4 6 3 7 2 1 8 t

Find all angle measures t 1131 67 672 3113 1135 67 8 67 6 113 7 180 - 67

LINES AND ANGLES Part II: Equations

Alternate Exterior Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x t 125 5 x = 125 5 5 x = 25

Corresponding Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x t 2 x + 1 151 2 x + 1 = 151 -1 -1 2 x = 150 2 2 x = 75

Consecutive Interior Angles • Name the angle relationship • Are they congruent or supplementary? supp • Find the value of x t 81 7 x + 15 + 81 = 180 7 x + 96 = 180 - 96 7 x = 84 7 7 x = 12

Alternate Interior Angles • Name the angle relationship • Are they congruent or supplementary? • Find the value of x t 3 x 2 x + 20 = 3 x - 2 x 20 = x

Homework • Honors Class: pg. 13 -14 (1 - 12) • All Other Common Core Classes: pg. 13 -14 (1 - 7, 9, 11, 12) • www. ixl. com Q 1