Notes 5 3 Parallel Lines Plane a surface

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Notes 5. 3 Parallel Lines

Notes 5. 3 Parallel Lines

Plane a surface such that if any two points on the surface are connected

Plane a surface such that if any two points on the surface are connected by a line, all points of the line are also on the plane. Coplanar – lie on the same plane. Noncoplanar – Do not lie on the same plane.

PARALLEL LINES Definition: lines that do not intersect. B l A m D C

PARALLEL LINES Definition: lines that do not intersect. B l A m D C Notation: l || m AB || CD

PERPENDICULAR LINES Def: Lines that intersect to form a right angle. m Notation: m

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

Transversal A line that intersects 2 lines at 2 different points. Forms 8 different

Transversal A line that intersects 2 lines at 2 different points. Forms 8 different angles. 1 3 7 4 6 5 8 2

Two angles that share the same vertex and whose sides are formed by

Two angles that share the same vertex and whose sides are formed by opposite rays. t 1 2 3 4 5 6 7 8 1 4 2 3 5 8 6 7

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

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

Supplementary Angles a. k. a: “Linear Pair” Two angles that together form a line

Supplementary Angles a. k. a: “Linear Pair” Two angles that together form a line (sum=180 ) 1+ 2=180 2+ 4=180 4+ 3=180 3+ 1=180 t 1 7 2 3 4 5 6 8 5+ 6=180 6+ 8=180 8+ 7=180 7+ 5=180

Supplementary Angles/ a. k. a. : Linear Pair Find the measures of the missing

Supplementary Angles/ a. k. a. : Linear Pair Find the measures of the missing angles: t 108? 72 108 ? 180 - 72

Two angles that occupy corresponding positions. t Top Left Top Right 1 3

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 1 5 2 6 3 7 4 8

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

Corresponding Angles Find the measures of the missing angles: t 35 145 ? Top Left ! Top Right ! 145 ? 35

Two angles that lie between parallel lines on opposite sides of the transversal

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

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

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

Pairs of angles that lie outside parallel lines on opposite sides of the transversal

Pairs of angles that lie outside parallel lines on opposite sides of the transversal t 1 2 3 4 5 6 7 8 2 7 1 8

Alternate Exterior Angles Find the measures of the missing angles: t 60⁰ 120 ?

Alternate Exterior Angles Find the measures of the missing angles: t 60⁰ 120 ? ? 60 120

Consecutive Interior Angles are Supplementary Two pairs of angles between parallel lines on the

Consecutive Interior Angles are Supplementary Two pairs of angles between parallel lines on the same sides of the transversal t 1 2 3 4 5 6 7 8 3 + 5 = 180 4 + 6 = 180

(Consecutive Interior Angles cont’d) Same - Side Interior Angles Same-Side Interior Angles and these

(Consecutive Interior Angles cont’d) Same - Side Interior Angles Same-Side Interior Angles and these angles are supplementary! These angles are also known as : t 1 2 3 4 5 6 7 8 3 + 5 = 180 4 + 6 = 180

Consecutive Interior Angles a. k. a. : Same-Side Interior Angles Find the measure of

Consecutive Interior Angles a. k. a. : Same-Side Interior Angles Find the measure of the missing angle: t 135 45 ? 180 - 135