Use the property to complete the statement. (Lesson 2.4)
37. Statements (Reasons)
1. å1 • å3 (Vertical angles are
congruent)
2. å4 • å2 (Vertical angles are
congruent)
3. å1 and å4 are complementary
(Given)
4. må1 + må4 = 90° (Definition of
complementary)
5. må1 = må3 (Definition of
congruence)
6. må4 = må2 (Definition of
congruence)
7. må3 + må2 = 90° (Substitution
property of equality)
8. å3 and å2 are complementary
(Definition of complementary)
? . AB
25. Reflexive property of equality: AB = ? . DF = ED
26. Symmetric property of equality: If ED = DF, then ? .AB = DF
27. Transitive property of equality: If AB = AC and AC = DF, then 2x
? . }3}y
28. Division property of equality: If 2x = 3y, then ᎏᎏ = z
z
? . 6 – 4 (or 2)
29. Subtraction property of equality: If x = 6, then x º 4 = Copy and complete the proof using the diagram and
the given information. (Lesson 2.5)
Æ
B
A
P
Æ
30. GIVEN 䉴 PD £ PC,
Æ
Æ
P is the midpoint of AC and BD
Æ
C
D
Æ
PROVE 䉴 AP £ BP
Statements
Reasons
Æ
Æ
Given
2. AP = PC
?
1. ?
2. 3. BP = PD
?
3. Definition of a midpoint
1. P is the midpoint of AC and BD.
?
4. Æ
Æ
Definition of a midpoint
4. Given
PD £ PC
5. PD = PC
?
5. ? AP = BP
6. Æ
Æ
7. AP £ BP
6. Transitive property of equality
7. Definition of congruent segments
Definition of congruent segments
In Exercises 31–32, use the diagram to complete the statement. (Lesson 2.6)
? are vertical angles. ™6
31. ™2 and 2
?. ™VWQ or ™RWU
32. ™QWR is supplementary to 33. In the diagram, suppose that ™3 and ™4 are complementary and that ™4 and
™5 are complementary. Prove that ™3 £ ™5. (Lesson 2.6)
™3 £ ™5 by the Congruent Complements Theorem
Solve for each variable. (Lesson 2.6)
34.
35.
(5c ⴙ 9)ⴗ
(7b ⴚ 20)ⴗ
r = 25; s = 10
A
GIVEN 䉴 ™1 and ™4 are complementary,
B
™DBE is a right angle.
PROVE 䉴 ™2 and ™3 are complementary.
See margin.
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Student Resources
U
W 3
7 5 4
6
T
(3r ⴙ 44)ⴗ (5s ⴙ 11)ⴗ
(8s ⴚ 19)ⴗ (5r ⴚ 6)ⴗ
(6c ⴚ 18)ⴗ
z = 13; x = 10
b = 8; c = 27
37. Write a two-column proof. (Lesson 2.6)
806
V
36.
(9b ⴚ 36)ⴗ
(8z ⴙ 12)ⴗ (5x ⴙ 14)ⴗ
(4z ⴙ 12)ⴗ (10x ⴙ 16)ⴗ
q
P
D
4
1
2
C
3
E
R
S
CHAPTER 3
G
Think of each segment in the diagram as part of a line.
Fill in the blank with parallel, skew, or perpendicular.
(Lesson 3.1)
¯
˘
¯
˘
¯
˘
¯
˘
¯
˘
¯
˘
E
F
H
?. parallel
1. HA and EC are ?. perpendicular
2. FD and AD are ?. skew
3. AD and GB are Think of each segment in the diagram as part of a line.
There may be more than one right answer. (Lesson 3.1)
¯
˘
¯
˘¯
˘¯
˘
4. Name a line parallel to AD . Sample answers: HF , BC , GE
¯
˘
B
A
C
D
¯
˘ ¯
˘¯
˘ ¯
˘
5. Name a line perpendicular to GB . Sample answers: AB , BC , GE , HG
¯
˘
¯
˘¯
˘ ¯
˘¯
˘
6. Name a line skew to EC . Sample answers: GH , AB , HF , AD
7. Name a plane parallel to GBC. Sample answers: HAD, ADF, DFH, FHA
Complete the statement with corresponding,
alternate interior, alternate exterior, or
consecutive interior. (Lesson 3.1)
7 8
6 5
? angles. corresponding
8. ™3 and ™7 are 3 4
2 1
? angles. alternate interior
9. ™4 and ™6 are ? angles. alternate exterior
10. ™8 and ™2 are ? angles. consecutive interior
11. ™4 and ™5 are ? angles. corresponding
12. ™5 and ™1 are 13. Fill in the blanks to complete the proof.
(Lesson 3.2)
GIVEN 䉴
A
D
Æ
Æ
AB fi BC,
Æ˘
BD bisects ™ABC
B
C
PROVE 䉴 m™ABD = 45°
Statements
Æ
Æ
1. AB fi BC
? ™ABC is a right ™.
2. 3. m™ABC = 90°
Æ˘
4. BD bisects ™ABC
5. m™ABD = m™DBC
6. m™ABD + m™DBC = 90°
Reasons
? Given
1. 2. Definition of perpendicular lines
? Definition of right ™
3. ? Given
4. ? Definition of ™ bisector
5. ? If 2 sides of 2 adj. acute Å are fi,
6. then the Å are complementary.
7. m™ABD + ? = 90°
m™ABD
8. 2(m™ABD) = 90°
7. Substitution property of equality
? Distributive property
8. 9. m™ABD = 45°
9. ? Division property of equality
Extra Practice
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