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Parallel Lines and Transversals
Angles and Parallel Lines Distance
Equations of Lines
Proving Lines are Parallel
Parallel Lines and Transversals for $100
Define: Skew lines
Answer
Skew Lines - Lines that are not coplanar and do not intersect
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Parallel Lines and Transversals for $200
Define: Parallel Lines
Answer
Parallel Lines – Lines that are coplanar and do not intersect.
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Parallel Lines and Transversals for $300
Define: Transversal
Answer
Transversal – A line that intersects two or more lines in a plane at different points
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Parallel Lines and Transversals for $400
Name all the line segments parallel to AB
Answer
Back
CD, GH, EF
Parallel Lines and Transversals for $500
Name all of the line segments perpendicular to GC
Answer
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EG, GH, CA, CD
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
Answer
<4 and <5, <3 and <6Note: <4 + <5 = 180 degrees
Back
l m
n1 4
2 3
5 8
6 7
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
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
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
Answer
<4 and <6, <3 and <5
Note: <4 <6
Back
l m
n1 4
2 3
5 8
6 7
Angles and Parallel Lines for $400
Given r is parallel to t, find the measure of angle 6
Answer
Back
<2 = 135 degree angle – corresponding angles.
<2 and < 6 are supplementary
135 + < 6 = 180
<6 = 45 degrees
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.
Answer
Back
m<1 must be congruent to m<3 for p || q
6x = 7x – 20
20 = x
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)
AnswerPoint: (-2, -4)
m = -5
Slope-intercept Form:
y = mx + b
-4 = -5(-2) + b
-4 = 10 + b
-14 = b
Thus, y = -5x - 14
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Equations of Lines for $200
Write the equation of the line in slope-intercept form:
The line through points
(-2, 3) and (0, -1)
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
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Equations of Lines for $300
Write the equation of the line in point-slope form:
The line through points
(2, -3) and (-2, 3)
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)
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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
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
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Equations of Lines for $500
Graph the following line:
y = 3x - 2
Answer
3x - 2
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Proving Lines to be Parallel for $100
Which 2 lines are parallel?
a) 5y = -3x - 5
b) 5y = -1 – 3x
c) 3y – 2x = -1
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
Proving Lines to be Parallel for $200
Given: <3 is supplemental to <8
Prove: p || r
Answer
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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
Proving Lines to be Parallel for $300
Given: <1 is congruent to <5
Prove: p || r
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
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.
Answer
Back
No, they are different transversals, so there is no theorem to prove the sides are congruent
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
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.
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Distance for $100
Define: Distance between lines
Answer
Distance between lines: the shortest distance between the two lines
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Distance for $200
Given that two lines are equidistance from a third line, what can you conclude?
Answer
The two lines are parallel to each other
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Distance for $300
Define: equidistant
Answer
Equidistant: The distance between two lines measured along a perpendicular line to the lines is always the same.
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Distance for $400
What are the steps to find the distance between two parallel lines?
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
Distance for $500
Find the distance between the given parallel lines
y = 2x – 32x – y = -4
Answer
Back
d = √(9.8)
(See Homework Solution Online)
