3-5 Smartboard Notes and answers Reg...
Transcript of 3-5 Smartboard Notes and answers Reg...
35 Smartboard Notes and answers Reg Geo.notebook
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August 31, 2015
Sep 68:50 PM
Find the slope of a line.
Use slopes to identify parallel and perpendicular lines.
Objectives
Sep 68:50 PM
The slope of a line in a coordinate planeis a number that describes the steepness of the line. Any two points on a line can be used to determine the slope.
35 Smartboard Notes and answers Reg Geo.notebook
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August 31, 2015
Sep 68:50 PM
Example 1A: Finding the Slope of a Line
Use the slope formula to determine the slope of each line.
AB
AC
AD
CD
A(2, 7), B(3, 7), C(4,2), D(2, 1)
Sep 68:50 PM
One interpretation of slope is a rate of change. If y represents miles traveled and x represents time in hours, the slope gives the rate of change in miles per hour.
35 Smartboard Notes and answers Reg Geo.notebook
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August 31, 2015
Sep 68:50 PM
Example 2: Transportation Application
Justin is driving from home to his college dormitory. At 4:00 p.m., he is 260 miles from home. At 7:00 p.m., he is 455 miles from home. Graph the line that represents Justin’s distance from home at a given time. Find and interpret the slope of the line.
Miles
Hour
Sep 68:50 PM
Check It Out! Example 2
What if…? Use the graph below to estimate how far Tony will have traveled by 6:30 P.M. if his average speed stays the same.
Since Tony is traveling at an average speed of 60 miles per hour, by 6:30 P.M. Tony would have traveled 390 miles.
First, read Example 2 on page 183.
35 Smartboard Notes and answers Reg Geo.notebook
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August 31, 2015
Sep 69:06 PM
Parallel Lines Theorem:Two nonvertical lines are parallel if and only if they have the same slope.Any two vertical lines are parallel. (Their slopes are undefined.)
Perpendicular Lines Theorem:Two nonvertical lines are perpendcular if and only if their slopes are negative reciprocals.Vertical and horizontal lines are perpendicular. (Vertical line has undefined slope (or no slope) and horizontal line has slope of zero.)
Sep 68:50 PM
Example 3A: Determining Whether Lines Are Parallel, Perpendicular, or Neither
Use slopes to determine whether the lines are parallel, perpendicular, or neither.
UV and XY for U(0, 2), V(–1, –1), X(3, 1), and Y(–3, 3)
35 Smartboard Notes and answers Reg Geo.notebook
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August 31, 2015
Sep 68:50 PM
Example 3B: Determining Whether Lines Are Parallel, Perpendicular, or Neither
Use slopes to determine whether the lines are parallel, perpendicular, or neither.
GH and IJ for G(–3, –2), H(1, 2), I(–2, 4), and J(2, –4)
Sep 68:50 PM
Example 3C: Determining Whether Lines Are Parallel, Perpendicular, or Neither
Use slopes to determine whether the lines are parallel, perpendicular, or neither.
CD and EF for C(–1, –3), D(1, 1), E(–1, 1), and F(0, 3)
35 Smartboard Notes and answers Reg Geo.notebook
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August 31, 2015
Sep 68:50 PM
Check It Out! Example 3a
Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither.WX and YZ for W(3, 1), X(3, –2), Y(–2, 3), and Z(4, 3)
Vertical and horizontal lines are perpendicular.
Sep 68:50 PM
Check It Out! Example 3b
Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither.KL and MN for K(–4, 4), L(–2, –3), M(3, 1), and N(–5, –1)
The slopes are not the same, so the lines are not parallel. The product of the slopes is not –1, so the lines are not perpendicular.
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August 31, 2015
Sep 68:50 PM
Check It Out! Example 3c
Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither.
BC and DE for B(1, 1), C(3, 5), D(–2, –6), and E(3, 4)
The lines have the same slope, so they are parallel.
Sep 69:21 PM
Assignment(p. 185) 217 (Only graph #6 and #14)
ANDCorresponding Angles Worksheet
35 Smartboard Notes and answers Reg Geo.notebook
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August 31, 2015
Sep 79:36 AM