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Answer Key
Chapter 3
Lesson
3.2
Challenge: Skills and Applications
1. Sample answer:
Statements
Reasons
1. POT and TOS
1. Given
4. Sample answer:
5. Sample answer:
Q
Y
P
20
are a linear pair.
W
45
50
2. POT TOS
↔ ↔
3. PS QT
to form a linear pair
of congruent angles,
then the lines are
perpendicular.
are complementary.
Z
R
2. Given
3. If two lines intersect
4. QOR and ROS
X
O
4. If two sides of two
adjacent acute angles
are perpendicular,
then the angles are
complementary.
6. Sample answer:
Note that DEF is
a straight angle.
G
D
7. Sample answer:
D
G
E
F
8. Sample answer: This
situation is possible in
three dimensions.
r
F
45 45
2. Sample answer: Since jk, 2 and 3 are
complementary by Theorem 3.2 (if two sides of
two adjacent acute angles are perpendicular, then
the angles are complementary). Therefore,
m2 m3 90. Since 1 3, we know
that m1 m3, so, by substitution,
m2 m1 90. By the Angle Addition
Postulate, mMON 90. Since MON is a
right angle, mn.
3. Sample answer:
1 and 2 are
complementary.
Given
1 and 4 are
complementary.
Given
Given
2≅ 4
≅ Complements
Theorem
m 2=m 4
Definition of ≅
4 and 3 are
complementary.
m 4 + m 3 = 90°
Definition of
complementary ’s
m 2 + m 3 = 90°
’s
m ABC = m 2 + m 3
Addition Postulate
Substitution property
of equality
m ABC = 90°
Substitution property
of equality
ABC is a right
Definition of right
AB BC
Definition of
’s
E
q
p
9. Sample answer: Lines AC and BC both contain
C and are perpendicular to j, so by the
Perpendicular Postulate they are the same line.
Points A and B can each be described as the intersection of this line and line j, so they must be the
same point, but this contradicts the given information. (Recall Postulate 7: If two lines intersect,
then their intersection is exactly one point.)
Therefore, the situation is not possible.