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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.
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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.
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What is “slope”? “STEEPNESS” of a line. What is positive slope?
What is negative slope?
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Formula for Slope
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Find the slope of the line containing the given points.
(1,2) and (3,6)
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Find the slope of the line containing the given points.
(1,2) and (3,6)
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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.
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Slope Find the slope of the line connecting the points (4,3) and (4,9)? The slope is undefined. It is a vertical line.
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Formula for a Line Y-INTERCEPT SLOPE
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Example: State the slope and y-intercept of the equation.
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Slope – Other Lines Find the slope of PQ, RS, and 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
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Slope – Parallel Lines Parallel lines have equal slopes.
jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt
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Slope – Other Lines 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
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Slope – Perpendicular Lines
Perpendicular lines have slopes which are negative reciprocals of each other. Horizontal and vertical lines are perpendicular to each other.
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Slope – Example #4 Points R(3, -2) and S(-1, 3) form a line.
a) find the slope of RS. 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
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Theorem 2-5 Two lines parallel to a third line are parallel to each other.
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Theorem 2-6 In a plane, two lines perpendicular to a third line are parallel to each other.
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Homework Homework Packet: Parallel and Perpendicular Lines
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