3.3, 3.6 & 3.7 Parallel and Perpendicular lines

7.0 Students prove and use theorems involving the properties of parallel

lines cut by a transversal

What are the characteristics of parallel lines and perpendicular lines?

• Parallel Lines:– Slopes are the same– Different y-intercept

• Perpendicular Lines:– Slopes are opposite-reciprocal– Y-intercept doesn’t matter

Parallel Theorem 1

• If two lines are parallel to the same line, then they are parallel to each other

• Ex:• If a//b and b//c, then a//c

Parallel Theorem 2

• In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

• Ex: Shown on interwrite

Parallel Theorem 3

• In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other

• Ex: Shown on interwrite

Practice

• What is the relationship between line a and line d?

dccbba

dccbba

dccbba

dccbba

,//,

//,,//

,,

//,//,

Short Assignment

• Pg 144 #14-21

Reviewing Graphing Parallel and Perpendicular lines

• Slope-intercept form

• Standard form

• Point-slope form)( 11 xxmyy

bmxy

CByAx

Slope-intercept form

• M= slope• B= y-intercept

bmxy

Graphing using slope-intercept form

Standard Form

• Uses x and y intercept to find 2 points

• X-intercept– When y=0– (# , 0)

• Y-intercept– When x=0– (0 , #)

CByAx

Point-Slope form

21

21

xx

yym

)( 11 xxmyy

Finding Equation using 2 points

• (0,5) (5,8) )( 11 xxmyy

• (8,10) (-4,2) )( 11 xxmyy

• (2,-6) slope -9 )( 11 xxmyy

Assignment

• Pg 169 #2, 4, 6, 8, 18, 20, 24, 26

Are these lines parallel, perpendicular or intersecting?

• Y=2x-5• Y=2x

Are these lines parallel, perpendicular or intersecting?

xy

xy

3

4

54

3

Are these lines parallel, perpendicular or intersecting?

• 3x+4y=12

• 6x+8y=24

Are these lines parallel, perpendicular or intersecting?

• Y-7x=6• Y+7x=8

Are these lines parallel, perpendicular or intersecting?

• (0,-2)(4,-4) and (4,1)(1,-5)

Are these lines parallel, perpendicular or intersecting?

• (0,3)(4,1) and (-6,1)(0,-2)

Assignment

• Pg 177 #4, 8, 10, 12, 16, 20