$100 $200 $300 $400 $500 $200 $300 $400 $500 parallel lines and transversals angles and parallel...
TRANSCRIPT
![Page 1: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/1.jpg)
![Page 2: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/2.jpg)
$100 $100 $100 $100 $100
$200
$300
$400
$500
$200 $200 $200 $200
$300 $300 $300 $300
$400 $400 $400 $400
$500 $500$500 $500
Parallel Lines and Transversals
Angles and Parallel Lines Distance
Equations of Lines
Proving Lines are Parallel
![Page 3: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/3.jpg)
Parallel Lines and Transversals for $100
Define: Skew lines
![Page 4: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/4.jpg)
Answer
Skew Lines - Lines that are not coplanar and do not intersect
Back
![Page 5: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/5.jpg)
Parallel Lines and Transversals for $200
Define: Parallel Lines
![Page 6: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/6.jpg)
Answer
Parallel Lines – Lines that are coplanar and do not intersect.
Back
![Page 7: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/7.jpg)
Parallel Lines and Transversals for $300
Define: Transversal
![Page 8: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/8.jpg)
Answer
Transversal – A line that intersects two or more lines in a plane at different points
Back
![Page 9: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/9.jpg)
Parallel Lines and Transversals for $400
Name all the line segments parallel to AB
![Page 10: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/10.jpg)
Answer
Back
CD, GH, EF
![Page 11: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/11.jpg)
Parallel Lines and Transversals for $500
Name all of the line segments perpendicular to GC
![Page 12: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/12.jpg)
Answer
Back
EG, GH, CA, CD
![Page 13: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/13.jpg)
Angles and Parallel Lines for $100
Identify two pairs of consecutive interior angles in the following drawing given l || m:
l m
n1 4
2 3
5 8
6 7
![Page 14: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/14.jpg)
Answer
<4 and <5, <3 and <6Note: <4 + <5 = 180 degrees
Back
l m
n1 4
2 3
5 8
6 7
![Page 15: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/15.jpg)
Angles and Parallel Lines for $200
Identify two pairs of corresponding angles in the following drawing given l || m:
l m
n1 4
2 3
5 8
6 7
![Page 16: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/16.jpg)
Answer
1 and 5, 4 and 8, 2 and 6, 3 and 7
NOTE: 1 5
Back
l m
n1 4
2 3
5 8
6 7
![Page 17: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/17.jpg)
Angles and Parallel Lines for $300
Identify two pairs of alternate interior angles in the following drawing given l || m:
l m
n1 4
2 3
5 8
6 7
![Page 18: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/18.jpg)
Answer
<4 and <6, <3 and <5
Note: <4 <6
Back
l m
n1 4
2 3
5 8
6 7
![Page 19: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/19.jpg)
Angles and Parallel Lines for $400
Given r is parallel to t, find the measure of angle 6
![Page 20: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/20.jpg)
Answer
Back
<2 = 135 degree angle – corresponding angles.
<2 and < 6 are supplementary
135 + < 6 = 180
<6 = 45 degrees
![Page 21: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/21.jpg)
Angles and Parallel Lines for $500
m<1 = 6x, and m<3 = 7x - 20. Find the value of x for p to be parallel to q. The diagram is not to scale.
![Page 22: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/22.jpg)
Answer
Back
m<1 must be congruent to m<3 for p || q
6x = 7x – 20
20 = x
![Page 23: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/23.jpg)
Equations of Lines for $100
Write the equation of the line in slope-intercept form:
The line with a slope of -5 through point (-2, -4)
![Page 24: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/24.jpg)
AnswerPoint: (-2, -4)
m = -5
Slope-intercept Form:
y = mx + b
-4 = -5(-2) + b
-4 = 10 + b
-14 = b
Thus, y = -5x - 14
Back
![Page 25: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/25.jpg)
Equations of Lines for $200
Write the equation of the line in slope-intercept form:
The line through points
(-2, 3) and (0, -1)
![Page 26: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/26.jpg)
Answer
Point: (-2, 3) Point: (0, -1)
m = (y2 – y1)/(x2 – x1)m = (-1- 3)/(0 – -2) = -4/2 = -2Slope-intercept Form:y = mx + b-1 = -2(0) + b-1 = bThus, y = -2x - 1
Back
![Page 27: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/27.jpg)
Equations of Lines for $300
Write the equation of the line in point-slope form:
The line through points
(2, -3) and (-2, 3)
![Page 28: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/28.jpg)
Answer
Points: (2, -3) and (-2, 3)
m = (y2 – y1)/(x2 – x1)m = (3- -3)/(-2 – 2) = 6/-4 = -3/2Point-Slope Form:
y – y1 = m(x – x1)
where (x1, y1) is a point on the lineThus, the equation of the line isy – 3 = -3/2(x - -2)y – 3 = -3/2(x + 2)
Back
![Page 29: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/29.jpg)
Equations of Lines for $400
Write the equation of a line perpendicular to the given line that intersects the given line on the y-axis. Write your answer in point-slope form:
y = 3x - 8
![Page 30: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/30.jpg)
Answery = 3x – 8So, m = 3, a point on the line = (0,-8)Point-Slope Form:
y – y1 = m(x – x1) y - -8 = 3(x – 0)y + 8 = 3xSlope of the Perpendicular line: (-1/3)y + 8 = (-1/3)x
Back
![Page 31: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/31.jpg)
Equations of Lines for $500
Graph the following line:
y = 3x - 2
![Page 32: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/32.jpg)
Answer
3x - 2
Back
![Page 33: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/33.jpg)
Proving Lines to be Parallel for $100
Which 2 lines are parallel?
a) 5y = -3x - 5
b) 5y = -1 – 3x
c) 3y – 2x = -1
![Page 34: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/34.jpg)
Answer
Back
Writing the lines in slope-intercept form:
a) 5y = -3x – 5
y = (-3/5)x – 1
b) 5y = -1 – 3x
y = (-3/5)x – (1/5)
c) 3y – 2x = -13y = 2x – 1y = (2/3)x – (1/3)
a||b
![Page 35: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/35.jpg)
Proving Lines to be Parallel for $200
Given: <3 is supplemental to <8
Prove: p || r
![Page 36: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/36.jpg)
Answer
Back
Statements Reasons<3 is supplemental to <8 Given
<3 + <8 = 180 Def. of Supplemental angles
<3 + <4 = 180 Def of Supplementary angles
<4 is congruent to <8 Theorem: Two angles supplementary to the same angle are congruent
<4 and <8 are corresponding angles
Definition of corresponding angles
p || r Theorem: If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
![Page 37: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/37.jpg)
Proving Lines to be Parallel for $300
Given: <1 is congruent to <5
Prove: p || r
![Page 38: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/38.jpg)
Answer
Back
Statements Reasons<1 is congruent to <5 Given
<4 is congruent to <1 Vertical Angles<4 <1 and <1 <5 thus, <4 <5
Transitive property of angle congruence
Thus, p || r Theorem: If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel
![Page 39: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/39.jpg)
Proving Lines to be Parallel for $400
Suppose you have four pieces of wood like those shown below. If b = 40 degrees can you construct a frame with opposite sides parallel? Explain.
![Page 40: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/40.jpg)
Answer
Back
No, they are different transversals, so there is no theorem to prove the sides are congruent
![Page 41: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/41.jpg)
Proving Lines to be Parallel for $500
Write a paragraph proof of this theorem: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Given: r is perpendicular to s, t is perpendicular to sProve: r || t
![Page 42: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/42.jpg)
AnswerBy the definition of perpendicular, r ┴ s
implies m<2 = 90, and t ┴ s implies m<6 = 90. Line s is a transversal. <2 and <6 are corresponding angles. By the Converse of the Corresponding Angles Postulate, r || t.
Back
![Page 43: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/43.jpg)
Distance for $100
Define: Distance between lines
![Page 44: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/44.jpg)
Answer
Distance between lines: the shortest distance between the two lines
Back
![Page 45: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/45.jpg)
Distance for $200
Given that two lines are equidistance from a third line, what can you conclude?
![Page 46: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/46.jpg)
Answer
The two lines are parallel to each other
Back
![Page 47: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/47.jpg)
Distance for $300
Define: equidistant
![Page 48: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/48.jpg)
Answer
Equidistant: The distance between two lines measured along a perpendicular line to the lines is always the same.
Back
![Page 49: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/49.jpg)
Distance for $400
What are the steps to find the distance between two parallel lines?
![Page 50: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/50.jpg)
Answer
Back
1) Write both lines in slope-intercept form
2) Find the equation of a line perpendicular to the two parallel lines
3) Find the intersection of the perpendicular line with each of the given two lines
4) Find the distance between the two points
![Page 51: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/51.jpg)
Distance for $500
Find the distance between the given parallel lines
y = 2x – 32x – y = -4
![Page 52: $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are](https://reader035.vdocuments.us/reader035/viewer/2022062305/5697bfb61a28abf838c9e394/html5/thumbnails/52.jpg)
Answer
Back
d = √(9.8)
(See Homework Solution Online)