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Parallel and Perpendicular Lines
Geometry
G.GPE.B.5 Prove that slope criteria for parallel and perpendicular lines
and use them to solve geometric problems.
Today’s Objectives
• To recall the equation for finding the slope of a line.
• To determine if lines are parallel, perpendicular, or neither based on their slopes.
What is “slope”?
• “STEEPNESS” of a line.
• What is positive slope?
• What is negative slope?
Formula for Slope
12
12
xx
yym
Find the slope of the line containing the given points.
(1,2) and (3,6)
12
12
xx
yym
12
26
xxm
Find the slope of the line containing the given points.
(1,2) and (3,6)
12
26
xxm
13
26
m
21
2
2
4m
Slope
• What is the slope of a line connecting the points (-2,3) and (4,3)?
• The slope of the line is 0. It is a horizontal line.
Slope
• Find the slope of the line connecting the points (4,3) and (4,9)?
• The slope is undefined. It is a vertical line.
Formula for a Line
bmxy SLOPE
Y-INTERCEPT
Example: State the slope and y-intercept of the equation.
43 xySlope = 3
y-intercept = 4
xy 24 Slope = -2
y-intercept = 4
Slope – Other Lines
Find the slope of PQ, RS, and TU.
13
133
m of PQ
m of RS
m of TU
What can be said about lines PQ and RS?
The lines are parallel and have the same slope.
jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt
Slope – Parallel Lines
Parallel lines have equal slopes.
jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt
Slope – Other Lines
13
133
m of PQ
m of RS
m of TU
What can be said about lines PQ and TU?
The lines are perpendicular and have slopes which multiply to -1.
jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt
Slope – Perpendicular Lines
Perpendicular lines have slopes which are negative reciprocals of each other.
Horizontal and vertical lines are perpendicular to each other.
Slope – Example #4
Points R(3, -2) and S(-1, 3) form a line.
a) find the slope of RS.3 ( 2) 5 5
41 3 4m
b) find the slope of a line perpendicular to RS.
Since perpendicular lines have slopes which are negative reciprocals, the slope of the perpendicular line is 4/5.
jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt
Theorem 2-5
Two lines parallel to a third line are parallel to each other.
Theorem 2-6
In a plane, two lines perpendicular to a third line are parallel to each other.
Homework
Homework Packet:
Parallel and Perpendicular Lines
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