5.2 I can prove segment and angle relationships
Angle Proof Worksheet #1
1. Given: B is the midpoint of AC
A
B
C
Prove: AB = BC
2. Given: AD is the bisector of
BAC B
D
A
C
Steps
1. B is the midpoint of AC
2. AB ≅ BC
3. AB = BC
Steps
1. AD is the bisector of BAC
2. BAD ≅ CAD
3. mBAD = mCAD
Reasons
Given
Definition of Congruent
Reasons
Given
Definition of Congruent
Prove: mBAD = mCAD
3. Given: D is in the interior of
BAC
B
D
A
Steps
1. D is in the interior of BAC
2. mBAD + mDAC = mBAC
Reasons
Given
C
Prove: mBAD + mDAC = mBAC
4. Given: mA + mB = 90° ; A ≅ C
Steps
1. mA + mB = 90°
2. A ≅ C
3. mA = mC
4.
Prove: mC + mB = 90°
5. Given: <1 and <2 form a straight angle
Prove: m1 + m2 = 180°
Reasons
Given
Given
Substitution steps 1 and
3
Steps
Reasons
1. <1 and <2 form a straight angle Given
2. mABC = 180°
Definition of Straight
Angle
3.
Angle Addition Postulate
4.
Substitution steps 2 and
3
6. Given: mEAC = 90°
E
B
1 2
A
D
3
C
Steps
1. mEAC = 90°
2.
3.
Reasons
Given
Angle Addition Postulate
Substitution steps 1 and
2
Prove: m1 + m2 + m3 = 90°
7. Given: m1 = 45° and m2 = 45°
D
B
1
A
2
C
Prove: AB is bisector of DAC
8. Given: HKJ is a straight angle
KI bisects HKJ
Prove: IKJ is a right angle
Steps
1. m1 = 45° and m2 = 45°
2. m1 = m2
3. 1 ≅ 2
4.
Steps
1. HKJ is a straight angle
2.
3. KI bisects HKJ
4. IKJ ≅ IKH
5. mIKJ = mIKH
6.
7. mIKJ + mIKJ = 180°
8. 2( mIKJ ) = 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: m2 + m1 = 90°
Steps
1. FD bisects EFC ; FC
bisects DFB
2. EFD ≅ DFC ,
DFC ≅ CFB
3.
4. mEFD = mCFB
5. EFD ≅ CFB
Steps
1. <WXY is a right angle
2. mWXY = 90°
3. m2 + m3 = mWXY
4. m2 + m3 = 90°
5. 1 ≅ 3
6. m1 = m3
7. m2 + m1 = 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 =
Reasons
Given
Definition of Congruent
Transitive Prop of =
Reasons
Given
Substitution steps 2 & 3
Given
Substitution steps 4 & 6