Angle Proof Worksheet #1
1. Given: B is the midpoint of AC
A
B
Steps
Given
1. B is the midpoint of AC
2. AB  BC
3. AB = BC
C
Prove: AB = BC
2. Given: AD is the bisector of
BAC
B
D
A
Reasons
C
Steps
1. AD is the bisector of
2. BAD  CAD
3. m BAD  m CAD
Definition of Congruent
Reasons
BAC
Given
Definition of Congruent
Prove: m BAD  m CAD
3. Given: D is in the interior of
BAC
B
D
Steps
1. D is in the interior of BAC
2. m BAD  m DAC  m BAC
Reasons
Given
C DAC  m BAC
Prove:A m BAD  m
4. Given: m A  m B  90 ;
A C
Steps
1. m A  m B  90
2. A  C
3. m A  m C
4.
Reasons
Given
Given
Substitution steps 1 and 3
Prove: m C  m B  90
5. Given: <1 and <2 form a straight
angle
Prove: m 1  m 2  180
Steps
1. <1 and <2 form a straight angle
2. m ABC  180
Reasons
Given
Definition of Straight Angle
3.
Angle Addition Postulate
4.
Substitution steps 2 and 3
6. Given: m EAC  90
E
1 2
A
D
Steps
1. m EAC  90
2.
Given
Angle Addition Postulate
C
3.
Substitution steps 1 and 2
B
3
Prove: m 1  m 2  m 3  90
Reasons
7. Given: m 1  45 and m 2  45
D
B
1
2
A
C
Prove: AB is bisector of
8. Given:
HKJ is a straight angle
KI bisects
Prove:
DAC
HKJ
IKJ is a right angle
Steps
1. m 1  45 and m 2  45
2. m 1  m 2
3. 1  2
4.
Steps
HKJ is a straight angle
1.
2.
3. KI bisects HKJ
4. IKJ  IKH
5. m IKJ  m IKH
6.
7. m IKJ  m IKJ  180
8. 2(m IKJ )  180
9.
10. IKJ is a right angle
9. Given: FD bisects EFC
FC bisects DFB
Prove:
EFD  CFB
10. Given: <WXY is a right angle
1 3
Prove: m 2  m 1  90
Reasons
Given
Substitution Prop. of =
Definition of angle
bisector
Reasons
Given
Definition straight angle
Given
Defintion of congruent
Angle Addition Postulate
Substitution steps 2, 5,
and 6
Simplify
Division Prop of =
Steps
1. FD bisects EFC ; FC
bisects DFB
2. EFD  DFC ,
DFC  CFB
3.
4. m EFD  m CFB
5. EFD  CFB
Steps
1. <WXY is a right angle
2. m WXY  90
3. m 2  m 3  m WXY
4. m 2  m 3  90
5. 1  3
6. m 1  m 3
7. m 2  m 1  90
Reasons
Given
Definition of Congruent
Transitive Prop of =
Reasons
Given
Substitution steps 2 & 3
Given
Substitution steps 4 & 6