Name: ______________________
Date: ___________ Period: _____
Homework Chapter 2 Review
1. If a  b , and angles 1, 2, and 3 have a ratio of 1:3:1. What are the measures of
the three angles?
a
<1 = 18
1

2
<2 = 54
3
<3 = 18
b
2. On a graph, point M is at (0, -2). Point M is then rotated 90 clockwise about the
origin to point M’. What are the coordinates of M’?
(-2, 0)
A
3. Given: AT is perpendicular to MH
Prove: 1 2 (This proof takes more than 2 steps!)
Statement
Reason
1. AT  MH
2. <1 is rt<
3. <2 is rt <
4. 1  2
Given
Def of perp
Def of perp
Euclid 4
1
M
2
H
T
4. Given: EB and BR trisect angle ZBS
BA bisects angle RBS
R
E
Prove EB ┴ BA using a paragraph proof.
From the diagram, ZBS is 180. Given that EB and BR
trisect <ZBS, <ZBE, <EBR, and <RBS all = 60. We are
also given that BA bisects <RBS. Since <RBS = 60,
<RBA is 30. since <EBR + <RBA = <EBA, <EBA = 90
which means it’s sides EB and BA are perpendicular.
5. Given: <1 is complementary to <3
and BC bisects <DBE
A
Z
S
B
A
D
Prove: <ABC is a right angle.
Statement
1. <1 is comp <3
2. BC bisects <DBE
3. <3 = <DBC
4. <1 + <3 = 90
5. <1 + <DBC = 90
6. <ABC is a rt <
6. <ABC is a rt <
Reason
Given
Given
Def of Bisect
Def of comp
Substitution
Def of rt <
Def of rt <
1
C
B
3
E
Name: ______________________
Date: ___________ Period: _____
6. Given: <1 = 35° 26’ 10’’
<2 = 54° 33’ 50’’
Prove: CD ┴ DE
Statement
1. <1 = 35° 26’ 10’’
2. <2 = 54° 33’ 50’’
3. <1 + <2 = 90
4. <CDE is rt <
5. CD ┴ DE
Reason
Given
Given
Addition
Def of rt <
1
2
Def of Perp
7. Two times the supplement of an angle is equal to 15 more than five times the
complement of the angle. Find the measure of the angle, its complement, and its
supplement.
x = 35
complement is 55
supplement is 145
8. Given: <1 ≅ <3
Conclusion:_______________
<3 is complementary to <4
<1 is complementary to <2
9. Given: <1 = (x2 + 5x - 30)
<3 = (45-5x)
Find: m<1
m<1 is 120 and m<1 is 20
1
Statement
1. 1  3
2. <3 comp <4
3. <1 comp <2
4. 2  4
2
4
3
Reason
Given
Given
Given
<’s comp to congruent <’s are congruent
(Cong Comp < Thm)
Name: ______________________
Date: ___________ Period: _____
10. Given: AB ┴ BC
≅
DE ┴ EF
<DEB ≅ <EBC
Prove : <FEB
Statement
1. AB  BC
2. <ABC is rt
3. DE  EF
4. <DEF is rt
5. <ABC = <DEF
6. <DEB = <EBC
7. <ABC - <EBC = <ABE
A
E
D
<ABE
F
Reason
Given
Def of Perp
Given
Def of perp
Rt <’s are congruent
Given
Subtraction
Statement
8. <DEF - <DEB = <FEB
9. <ABE = <FEB
≅
11. Given: 1 2
<NAP
<SPA
<3 = <4
Conclusion:______________


Statement
1. 1 2
2. <NAP = <SPA
3. <NAP - <1 = <3
4. <SPA - <2 = <4
5. <3 = <4
1
A
Statement
1. <BAD = <FAD 
2. <BAC = <FAE
3. <BAD - <BAC = <CAD
4. <FAD - <FAE = <EAD
5. <CAD = <EAD
6. AD bisects <CAE
N
S
3
4
Reason
Given
Given
Subtraction
Subtraction
Subtraction Prop of Equality
Def of bisect
Reason
Subtraction
Subtraction Prop of Equal
2
Reason
Given
Given
Subtraction
Subtraction
Subtraction Prop of Equality
12. Given: BAD  FAD
BAC  FAE
Conclusion: AD bisects CAE


C
B
P
Name: ______________________
Date: ___________ Period: _____
13. Given:
RO = 3cm
CK = 3cm
O
R
C
K
Prove: RC is congruent to OK
Statement
1. RO is 3
2. CK is 3
3.
Reason
Given
Given
RC  OK
Addition Prop of Equality
True or False:
___T__ 14. The supplement of an acute angle is obtuse.
____T_ 15. The x-axis is perpendicular to the y-axis.
__T___ 16. If two angles are supplementary to congruent angles, then they are
congruent.
__F___ 17. If two angles are congruent to vertical angles, then they are
complementary.
___T__ 18. Point M(1,2) and D(5,4) are the same distance from Point I(3,3).
19. Find the reflection of Point X over the y-axis.
(-2,2)
(2, 2)
20. Given: <1 is complementary to <3
<2 is complementary to <4
3  4
Conclusion:______________
(2, 2)
Statement
1. <1 comp <3
2. <2 comp <4
3. 1  2
4. 3  4
Reason
Given
Given
Vertical <’s
<’s comp to congruent <’s are congruent
3
1
2
4
Name: ______________________
Date: ___________ Period: _____
21. Given: GR is congruent to EY
Diagram as shown.
GM  ET
Conclusion: ________________
(2, 2)
Statement
1.
2.
3.
4.
5.
GR  EY
MR  TY
GR  MR  GM
EY  TY  ET
GM  ET
E
G
T
M
Reason
Given
Assumed from Diagram
R
Subtraction
Subtraction
Subtraction Prop of Equality
22. <1 = 36° and <5 is complementary to <1. Find the missing angles.
<1 = 36
<2 = 144
<3 = 36
<4 = 144
<5 = 54
<6 = 126
<7 = 54
<8 = 126
8 5
7 6
4 1
3 2
Y