Parallel and Perpendicular Lines

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Presentation transcript:

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

Find the slope of the line containing the given points. (1,2) and (3,6)

Find the slope of the line containing the given points. (1,2) and (3,6)

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 Y-INTERCEPT SLOPE

Example: State the slope and y-intercept of the equation.

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

Slope – Parallel Lines Parallel lines have equal slopes. jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt

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

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. 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