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2. g || h ; Because e  g and e  h , lines g and
3.4 Practice A
h are parallel by the Lines Perpendicular to a
Transversal Theorem (Thm. 3.12).
1. about 5.7 units
2.
3.
3. none; The only thing that can be concluded from
the diagram is that  n and m  p. In order to
say that the lines are parallel, you need to know
something about the intersections of and p or
m and n.
4. yes; Because e || f , a  e and c  e , lines a
and c are perpendicular to line f by the
Perpendicular Transversal Theorem (Thm. 3.11).
Because a  f , b  f , c  f , and d  f , by
the Lines Perpendicular to a Transversal Theorem
(Thm. 3.12) and the Transitive Property of Parallel
Lines (Thm. 3.9), lines a, b, c, and d are all parallel
to each other.
4. b || c ; Because a  b and a  c , lines b and c
are parallel by the Lines Perpendicular to a
Transversal Theorem (Thm. 3.12).
5.
STATEMENTS
REASONS
1. 1  2
1. Given
2. e  h
2. Linear Pair
Perpendicular
Theorem (Thm. 3.10)
3. e || f
3. Lines Perpendicular
to a Transversal
Theorem (Thm. 3.12)
4. e || g
4. Transitive Property
of Parallel Lines
(Thm. 3.9)
6. no; There is only one perpendicular bisector that
can be drawn, but there is an infinite number of
perpendicular lines.
7. w || x, w || z, x || z ; Because w  b and
x  b, w || x by the Lines Perpendicular to a
Transversal Theorem (Thm 3.12). Because w  b
and z  b, w || z by the Lines Perpendicular to a
Transversal Theorem (Thm 3.12). Because w || x
and w || z, x || z by the Transitive Property of
Parallel Lines Theorem (Thm. 3.9).
3.4 Practice B
|| n, m || n, || m ; Because j  and
j  n , lines and n are parallel by the Lines
Perpendicular to a Transversal Theorem
(Thm. 3.12). Because k  m and k  n ,
lines m and n are also parallel by the Lines
Perpendicular to a Transversal Theorem
(Thm. 3.12). Because || n and m || n , lines
and m are parallel by the Transitive Property of
Parallel Lines Theorem (Thm. 3.9).
5.
STATEMENTS
REASONS
1. 1  2
1. Given
2. a  c
2. Linear Pair
Perpendicular
Theorem (Thm. 3.10)
3. c || d
3. Given
4. a  d
4. Perpendicular
Transversal Theorem
(Thm. 3.9)
5. b  d
5. Given
6. a || b
6. Lines Perpendicular to
a Transversal Theorem
(Thm. 3.12)
6. m1  90, m2  15, m3  90,
m4  45, m5  15; m1  90, because
it is vertical angles with a right angle, so it has the
same angle measure. m2  90  75  15,
because it is complementary to the 75 angle.
m3  90, because it is marked as a right angle.
m4  75  30  45, because together with
the 30 angle, the angles are vertical angles with
the 75 angle, so the angle measures are equal.
m5  15, because it is vertical angles with 2,
so the angles have the same measure.
1. 5 units
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Geometry
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A1
Answers
7.no; You do not know anything about the relationship
between lines x and y or x and z.
1
y  2 x and y   x have the same y-intercept
2
and the slopes are negative reciprocals.
3.5 Practice A
1. P3.5, 1
10. yes; Sample answer: The lines
2. P0, 14.2
 5
 2


11.   ,  2 
3. perpendicular; Because
 9  2 
m1  m2       1, lines 1 and 2 are
 2  9 
perpendicular by the Slopes of Perpendicular Lines
Theorem (Thm. 3.14).
 4  5 
 5  4 
and 2 are neither parallel nor perpendicular.
4. neither; Because m1  m2      1, lines 1
5. y  4x  7
7. y 
9. 2
1
x 8
3
2  2.83
6. y  6x  9
8. y  3x  8
10. 2
26  10.2
11. 62.5
12. no; For a line with a slope between 0 and 1, the
slope of a line perpendicular to it would be
negative.
13. 5, 4
3.5 Practice B
1. Q  1.5, 3
2. Q  0, 3
1
 1
3
 6
1 and 2 are neither parallel nor perpendicular.
3. neither; Because m1  m2  2     , lines
1
4
4. y  6x  10
5. y   x 
6. about 4.5
7. about 3.4
11
4
8. Sample answer: b  5, c  1
9. a. The slope is m2 , where 1  m2  0.
b. The slope is m3 , where m3  1.
c. The lines are perpendicular; They are
perpendicular by the Perpendicular Transversal
Theorem (Thm. 3.11).
A2
Geometry
Answers
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