3.3, 3.6 & 3.7 parallel and perpendicular lines 7.0 students prove and use theorems involving...
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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
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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
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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
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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
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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
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Practice
• What is the relationship between line a and line d?
dccbba
dccbba
dccbba
dccbba
,//,
//,,//
,,
//,//,
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Short Assignment
• Pg 144 #14-21
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Reviewing Graphing Parallel and Perpendicular lines
• Slope-intercept form
• Standard form
• Point-slope form)( 11 xxmyy
bmxy
CByAx
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Slope-intercept form
• M= slope• B= y-intercept
bmxy
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Graphing using slope-intercept form
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Standard Form
• Uses x and y intercept to find 2 points
• X-intercept– When y=0– (# , 0)
• Y-intercept– When x=0– (0 , #)
CByAx
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Point-Slope form
21
21
xx
yym
)( 11 xxmyy
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Finding Equation using 2 points
• (0,5) (5,8) )( 11 xxmyy
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• (8,10) (-4,2) )( 11 xxmyy
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• (2,-6) slope -9 )( 11 xxmyy
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Assignment
• Pg 169 #2, 4, 6, 8, 18, 20, 24, 26
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Are these lines parallel, perpendicular or intersecting?
• Y=2x-5• Y=2x
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Are these lines parallel, perpendicular or intersecting?
xy
xy
3
4
54
3
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Are these lines parallel, perpendicular or intersecting?
• 3x+4y=12
• 6x+8y=24
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Are these lines parallel, perpendicular or intersecting?
• Y-7x=6• Y+7x=8
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Are these lines parallel, perpendicular or intersecting?
• (0,-2)(4,-4) and (4,1)(1,-5)
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Are these lines parallel, perpendicular or intersecting?
• (0,3)(4,1) and (-6,1)(0,-2)
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Assignment
• Pg 177 #4, 8, 10, 12, 16, 20