provinglinesparallel slope of lines slope: the rise and run of a line to find slope, you use the...
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![Page 1: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/1.jpg)
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![Page 3: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/3.jpg)
![Page 4: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/4.jpg)
Proving Lines Parallel
![Page 5: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/5.jpg)
Slope of Lines
Slope: the rise and run of a line
To find slope, you use the following formula… y2 − y1𝑚 = x2 – x1
Ex. Find the slope between the given points.(-3, 5) and (6, -2)
−2 −5 −7=m = 6 −−3 9
![Page 6: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/6.jpg)
Types of Slope
1. Positive SlopeA positive number.
2. Negative Slope
A negative number.
3. No Slope 4. Zero SlopeZero divided by a number.
A number divided by zero.
![Page 7: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/7.jpg)
You try…
Find the slope between to given points.2.1. (2, -3) (-2, 8) (-8, -1) (-4, -3)
3. (8, -4) (0, 7) 4. (-5, 1) (-2, -2)
![Page 8: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/8.jpg)
You try…
Find the slope between to given points.2.1. (2, -3) (-2, 8) (-8, -1) (-4, -3)
3. (8, -4) (0, 7) 4. (-5, 1) (-2, -2)
![Page 9: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/9.jpg)
Find the slope of the parallel lines.(-4, 2) (-1, 3) 3 − 2 1𝑚 = =−1 − −4 3
(-1, 3)
(-4, 2)
(1, -5) (4, -4)−4 − −5 1𝑚 = =4 − 1 3(4, -4)
(1, -5)
So, the slope of parallel lines are always the SAME!!!
![Page 10: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/10.jpg)
Find the slope of the perpendicular lines.
(-5, -2) (-3, 1) 1 − −2 3𝑚 = =−3 − −5 2(-3, 1) (3, -4) (0, -2)−2 − −4 2 −2𝑚 = = =0 − 3 −3 3(0, -2)
(-5, -2)
(3, -4)
So, the slope of perpendicular lines are always OPPOSITE,RECIPORCALS!!!
![Page 11: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/11.jpg)
Determine whether line AB and line CD areparallel, perpendicular or neither.
1. A (-2, -5) B(4, 7) C(0, 2) D(8, -2) 2. A (-8, -7) B(4, -4) C(-2,-5) D(1, 7)
7−− 5 = 12 −4 −−7 = 3
1AB = = 2 AB = =4−−2 6 4−−8 12 4 − 2−2 = −4 1 7 −−5 12 CD = = − CD = = = 48−0 8 2 1−−2 3
Since the slopes
reciprocals, then
be PARALLEL.
are opposite,the lines would
Although the slopes are reciprocals,
they are not opposites, so these
lines would be NEITHER.
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You try…
Determine whether line AB and line CDneither.
are parallel, perpendicular or
1. A(-3, -2), B(9, 1), C(3, 6), D(5, -2)
2. A(-4, 0), B(0, 3), C(-4, -3), D(8, 6)
3. A(-10, 7), B(2, 1), C(4, 0), D(6, 1)
![Page 13: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/13.jpg)
You try…
Determine whether line AB and line CDneither.
are parallel, perpendicular or
1. A(-3, -2), B(9, 1), C(3, 6), D(5, -2)
2. A(-4, 0), B(0, 3), C(-4, -3), D(8, 6)
3. A(-10, 7), B(2, 1), C(4, 0), D(6, 1)
![Page 14: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/14.jpg)
Angles and Parallel Lines
…Recall
When a transversal crosses parallel linesalternate interior and correspondingangles are CONGRUENT.
To prove lines parallel,
determine what type of angle pair is shown, and put them equal to each other.
![Page 15: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/15.jpg)
Find the value of x so that the lines are parallel.
1. 5x + 5 = 45-5 -5
5x = 405
x = 8
5
2.
6x + 10 + 10x + 10 = 18016x + 20 = 180
- 2016x = 160
- 20
16x = 10
16
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You try…
Find1.
the value of x so that the lines2.
are parallel.
3. 4.
![Page 17: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/17.jpg)
You try…
Find1.
the value of x so that the lines2.
are parallel.
3. 4.
![Page 18: ProvingLinesParallel Slope of Lines Slope: the rise and run of a line To find slope, you use the following formula… y 2 − y 1 = x 2 – x 1 Ex. Find](https://reader035.vdocuments.net/reader035/viewer/2022070403/56649f285503460f94c4004d/html5/thumbnails/18.jpg)
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