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CP Geometry
Worksheet 2.7
X
1.
Given: 1 comp.
Prove: XA  XC
1 2
A
B
2
C
Given: 1  2
Prove: EG bisects
PEN
2.
P
G
KEY
Name:
E 2
1
4
1.
2.
3.
4.
5.
1.
2.
3
3.
4.
N
3.
Statements
1 comp. 2
1  2  90
1  2  AXC
AXC  90
XA  XC
Statements
1 2
1 3
2 4
3 4
EG bisects
PEN
1.
2.
3.
4.
5.
Reasons
Given
Def. Comp. Angles
Angle Add. Post.
Substitution
Def. Perp. Lines
Reasons
1. Given
2. Vertical Angles Th.
3. Trans./Substitution
4. Def. Angle Bisector
Statements
1
Reasons
3
1.
1 supp.
2. m 1  m
1  3;
3.
4. m 3  m
5.
3 supp.
4
2
Given:
Prove:
4.
1 supp.
3 supp.
2
4
Statements
1.
3 4
2.
1 3
3.
2 4
4.
1 2
5. RB bisects
1.
2.
3.
4.
ARC 5.
2
2  180
2 4
4  180
4
Reasons
Given
Vertical Angles Th.
Vertical Angles Th.
Trans./Substitution
Def. Angle Bisector
1.
2.
3.
4.
5.
Given
Def. Supp. Angles
Vertical Angles Th.
Substitution
Def. Supp. Angles
F
A
B
1
2
R
4
3
E
D
C
Given:
3 4
Prove: RB bisects
ARC
5.
Statements
3
4
1.
1
Given:
Prove:
2
1 2
1 3
4 2
6.
Statements
1
2; 1 
Reasons
3
1. Given
2.
2 3
2. Trans./Substitution
3.
3 4
3. Vertical Angles Th.
4.
2 4
4. Trans./Substitution
Reasons
1.
4 3
1. Given
2.
4 5
2. Vertical Angles Th.
3.
3 5
3. Trans./Substitution
4.
2 & 3 form LP 4. Def. Linear Pair
5.
2 supp.
6.
2  3  180
6. Def. Supp. Angles
7.
2  5  180
7. Substitution
8.
2 supp.
8. Def. Supp. Angles
3
5
5. Linear Pair Post.
2
Given:
Prove:
4
3
1
5
4 3
2 supp. 5
7.
Statements
Reasons
1. Given
1.
2 comp.
2.
2  3  90
2. Def. Comp. Angles
3.
2  3  ACB
3. Angle Add. Post.
4.
ACB  90
4. Trans./Substitution
5. CD  AB
6.
1  90
7.
ACB  1
3
C
2 3
1
A
D
5. Given
6. Def. Perp. Lines
7. Trans./Substitution
Given:
2 comp. 3
CD  AB
Prove: ACB  1
B
8. C
Statements
1.
2
1
A
B
Prove:
9.
ABC is a rt.
1 C
2 A
A comp. C
Given:
Prove:
4 5
4 supp.
1. Given
ABC is a rt.
2. m ABC  90
2. Def. Right Angles
3. m 1  m 2  m ABC
3. Angle Add. Post.
4. m 1  m 2  90
4. Trans./Substitution
5.
Given:
Reasons
1
C; 2 
A
5. Given
6. m C  m A  90
6. Substitution
7.
7. Def. Comp. Angles
A comp.
C
6
4
Statements
Reasons
1.
4 5
2.
5& 6 form LP 2. Def. Linear Pair
3.
5 supp.
1. Given
6
3. Linear Pair Post.
4. m 5  m 6  180
4. Def. Supp. Angles
5. m 4  m 6  180
5. Substitution
6.
6. Def. Supp. Angles
4 supp.
6
5
6
10.
1 4
2 3
Given:
Prove:
Statements
1 3
2
4
1.
1 4
1. Given
2.
1& 3 form LP
2. Def. Linear Pair
3.
2 & 4 form LP
3. Def. Linear Pair
4.
1 supp. 3
2 supp. 4
2 3
4. Linear Pair Post.
5.
Given: RP  q
1 comp.
Prove: 2  3
11.
3
Statements
P
1
3
2
1. RP  q ;
1 comp. 3
2.
1 comp. 2
q
R
3.
12.
Given:
Prove:
3
1 2
3 4
1
2
Given:
Prove:
3
2
1
1 supp.
1 3
5. Cong. Supp. Th.
Reasons
1. Given
2. Ext. sides of adj.
are  , then
s comp.
3. Cong. Comp. Th.
Reasons
1.
1 2
1. Given
2.
1& 3 form LP
2& 4 form LP
1 supp. 3
2 supp. 4
3 4
2. Def. Linear Pair
3.
4.
13.
2 3
Statements
4
Reasons
Statements
2
3. Linear Pair Post.
4. Cong. Supp. Th.
Reasons
1. Given
1.
1 supp.
2.
2 & 3 form LP
2. Def. Linear Pair
3.
2 supp.
3. Linear Pair Post.
4.
1 3
2
3
4. Cong. Supp. Th.
14.
Given:
1 comp. 2
3 comp. 4
Prove: m 1  m 4
Statements
2
3
4
15.
Given: OD  OB
OC  OA
Prove:
1 3
A
1
2
3
1. Given
4. m 2  m 3
4. Vertical Angles Th.
5. m 1  m 4
5. Subtraction
2. Def. Comp. Angles
3. Trans./Substitution
Statements
B
C
1 comp. 2
3 comp. 4
2. m 1  m 2  90
m 3  m 4  90
3. m 1  m 2  m 3  m 4
1.
1
Reasons
O
Reasons
1. OD  OB ; OC  OA
1. Given
2.
1 comp.
2. Def. Perp. Lines
3.
3 comp.
4.
1 3
2
2
3. Def. Perp. Lines
4. Cong. Comp. Th.
D
16.
JC  JD and
C
E
J
D
CJE . If m EJD  37 , then m K = 37º.
(Ext. sides of adj. are  , then
s comp. and Congruent
Complements Theorem)
K
m 1 m 2
m 3  5x  30
m 4  9x  50
17.
l
K is complementary to
3 1
2 4
Find m
m
m
m
1
50º
2
50º
3
130º
4
130º