LINES AND ANGLES PARALLEL LINES Def line that

LINES AND ANGLES

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

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

Ex. of Parallel Lines • Streets: N Laramie and N Leclaire

PERPENDICULAR LINES • Def: Lines that intersect to form a right angle. m • Illustration: Do Not Assume, You must be told it is a right angle!! n • Notation: m n • Key Fact: 4 right angles are formed.

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

Transversal • Def: a line that intersects two lines at t different points • Illustration: t t

Vertical Angles • Two angles that are only touching by a vertex (no sides) and are congruent angles. t 1 2 3 4 5 7 6 8

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 ) t 1 2 3 4 5 7 6 8

Supplementary Angles/ Linear Pair • Find the measures of the missing angles t 108? 72 108 ? 180 - 72 After finding one angle, the other is a Vertical angle to it!!!!

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 8 Bottom Right

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

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

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

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

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

Consecutive Interior Angles • Two angles that lie between parallel lines on the same sides of the transversal t 1 2 3 4 5 6 7 8

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

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