Transcript Geometry Jeapordy

Parallel Lines
and
Transversals
Angles and
Parallel Lines
Equations of
Lines
Proving
Lines are
Parallel
Distance
$100 $100 $100 $100 $100
$200 $200 $200 $200 $200
$300 $300 $300 $300 $300
$400 $400 $400 $400 $400
$500 $500 $500 $500 $500
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
CD, GH, EF
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Parallel Lines and Transversals for
$500
Name all of the line segments
perpendicular to GC
Answer
EG, GH, CA, CD
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Angles and Parallel Lines for $100
Identify two pairs of consecutive
interior angles in the following
drawing given l || m:
m
l
n
1
4
5
2
3
8
6
7
Answer
<4 and <5, <3 and <6
Note: <4 + <5 = 180 degrees
m
l
n
1
4
5
2
3
8
6
7
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Angles and Parallel Lines for $200
Identify two pairs of
corresponding angles in the
following drawing given l || m:
m
l
n
1
4
5
2
3
8
6
7
Answer
1 and 5, 4 and 8, 2 and 6, 3 and 7
NOTE: 1  5
m
l
n
1
4
5
2
3
8
6
7
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Angles and Parallel Lines for $300
Identify two pairs of alternate
interior angles in the following
drawing given l || m:
m
l
n
1
4
5
2
3
8
6
7
Answer
<4 and <6, <3 and <5
Note: <4  <6
m
l
n
1
4
5
2
3
8
6
7
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Angles and Parallel Lines for $400
Given r is parallel to t, find the
measure of angle 6
Answer
<2 = 135 degree angle – corresponding
angles.
<2 and < 6 are supplementary
135 + < 6 = 180
<6 = 45 degrees
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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
m<1 must be congruent to m<3 for p || q
6x = 7x – 20
20 = x
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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)
Answer
Point: (-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 = -2
Slope-intercept Form:
y = mx + b
-1 = -2(0) + b
-1 = b
Thus, 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 = -3/2
Point-Slope Form:
y – y1 = m(x – x1)
where (x1, y1) is a point on the line
Thus, the equation of the line is
y – 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
Answer
y = 3x – 8
So, m = 3, a point on the line = (0,-8)
Point-Slope Form:
y – y1 = m(x – x1)
y - -8 = 3(x – 0)
y + 8 = 3x
Slope 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
Writing the lines in slope-intercept form:
a) 5y = -3x – 5
y = (-3/5)x – 1
b) 5y = -1 – 3x
c) 3y – 2x = -1
3y = 2x – 1
y = (2/3)x – (1/3)
a||b
y = (-3/5)x – (1/5)
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Proving Lines to be Parallel for
$200
Given: <3 is supplemental to <8
Prove: p || r

Answer
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
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Proving Lines to be Parallel for
$300
Given: <1 is congruent to <5
Prove: p || r
Answer
Statements
Reasons
<1 is congruent to <5
Given
<4 is congruent to <1
Vertical Angles
<4 <1 and <1  <5 thus, Transitive property of angle
<4 <5
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
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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
No, they are different
transversals, so there is no
theorem to prove the sides are
congruent
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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 s
Prove: r || t
Answer
By 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
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
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Distance for $500
Find the distance between the
given parallel lines
y = 2x – 3
2x – y = -4
Answer
d = √(9.8)
(See Homework Solution Online)
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