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##### Warm up

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**5**6 4 7 8 3 2 t 1 Warm up List all pairs of angles that fit the description. • Corresponding • Alternate Interior • Alternate Exterior • Consecutive Interior**B**A D l C m 28 PARALLEL LINES • Def: line that do not intersect. • Illustration: • Notation:l || mAB|| CD p. 129**Examples of Parallel Lines**• Hardwood Floor • Opposite sides of windows, desks, etc. • Parking slots in parking lot • Parallel Parking • Streets: Laramie & LeClaire**Examples of Parallel Lines**• Streets: Belmont & School**m**n 29 PERPENDICULAR LINES • Def: Lines that intersect to form a right angle. • Illustration: • Notation:m n • Key Fact: 4 right angles are formed. p. 79**Ex. of Perpendicular Lines**• Window panes • Streets: Belmont and Cicero**30**Transversal • Def: a line that intersects two lines at different points • Illustration: t p. 131**Vertical Angles**• Two angles that are opposite angles. t • 14 • 2 3 • 5 8 • 6 7 1 2 4 3 6 5 7 8**Vertical Angles**• Find the measures of the missing angles t 125 ? 125 55 ? 55 **t**1 2 4 3 6 5 7 8 Supplementary Angles/Linear Pair • Two angles that form a line (sum=180) • 1+2=180 • 2+4=180 • 4+3=180 • 3+1=180 • 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 72 180 - 72 ? 108 **1**2 3 4 5 6 7 8 30 Corresponding Angles • Two angles that occupy corresponding positions. t • 15 • 2 6 • 3 7 • 4 8 Top Left Top Right Bottom Left Bottom Right Top Left Top Right Bottom Left Bottom Right p. 131 & 143**Corresponding Angles**• Find the measures of the missing angles t 145 35 ? 145 **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 InteriorAngles**• Find the measures of the missing angles t 82 82 98 ?**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 ExteriorAngles**• Find the measures of the missing angles t 120 ? 120 60 **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 InteriorAngles**• Find the measures of the missing angles t 180 - 135 135 45 ?**Corresponding**4 and 2 3 and 1 5 and 7 6 and 8 5 6 4 7 8 3 2 t 1**Alternate Interior**3 and 7 2 and 6 5 6 4 7 8 3 2 t 1**Alternate Exterior**5 and 1 4 and 8 5 6 4 7 8 3 2 t 1**Consecutive Interior**5 3 and 2 6 and 7 6 4 7 8 3 2 t 1**Find all angle measures**t 180 - 67 113 67 1 3 67 2 113 113 5 67 8 67 6 7 113 **LINES AND ANGLES**Part II: Equations**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