LINES AND ANGLES

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

Examples of Parallel Lines Hardwood Floor Opposite sides of windows, desks, etc. Parking slots in parking lot Parallel Parking

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

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

Vertically opposite Angles Two angles that are opposite angles. t 1   4 2   3 5   8 6   7 1 2 3 4 5 6 7 8

Vertically opposite Angles Find the measures of the missing angles t 125  ? 125  55  ? 55 

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

Linear Pair 180 - 72 Find the measures of the missing angles t ? ? 108  72  180 - 72 ? 108 

LINES AND ANGLES List all pairs of angles that fit the description. 1 2 3 4 5 6 7 8 t List all pairs of angles that fit the description. Corresponding Alternate Interior Alternate Exterior Consecutive Interior HIDDEN MESSAGE MAN . BOARD

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

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

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

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

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

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

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

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

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

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

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

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

Find all angle measures t 180 - 67 113  67  1 67  2 3 113  113  5 67  8 67  6 113  7

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

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

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

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