use the following for #27 & #28
given given definition of angle bisector definition of angle bisector definition of supplementary angles
given definition of supplementary angles linear pair (supplementary) theorem/postulate vertical angles congruent theorem definition of congruence.
given transitive property transitive property substitution property
27 given: $overline{km}$ bisects $angle jkn$, $overline{kn}$ bisects $angle mkl$
prove: $angle jkmcongangle nkl$
statements reasons
1. $overline{km}$ bisects $angle jkn$ 1.
2. $angle jkmcongangle mkn$ 2.
3. $overline{kn}$ bisects $angle mkl$ 3.
4. $angle mkncongangle nkl$ 4.
5. $angle jkmcongangle nkl$ 5.
28 given: $angle1$ and $angle2$ form a linear pair, $angle2congangle4$
prove: $angle1$ and $angle3$ are supplementary
statements reasons
1. $angle1$ and $angle2$ form a linear pair 1.
2. $angle1$ and $angle2$ are supplementary 2.
3. $mangle1 + mangle2=180^{circ}$ 3.
4. $angle2congangle4$ 4.
5. $angle3congangle4$ 5.
6. $angle2congangle3$ 6.
7. $mangle2 = mangle3$ 7.
8. $mangle1 + mangle3=180^{circ}$ 8.
9. $angle1$ and $angle3$ are supplementary 9.
© gina wilson (all things algebra®, llc). 2014 - 2020

Question

Accepted Answer

# Explanation:
## Step1: State given fact
Given
## Step2: Apply angle - bisector definition
Definition of Angle Bisector
## Step3: State given fact
Given
## Step4: Apply angle - bisector definition
Definition of Angle Bisector
## Step5: Use transitive property of congruence
Transitive Property of Congruence

# Answer:
| Statements | Reasons |
|--|--|
| 1. $\overline{KM}$ bisects $\angle{JKN}$ | 1. Given |
| 2. $\angle{JKM}\cong\angle{MKN}$ | 2. Definition of Angle Bisector |
| 3. $\overline{KN}$ bisects $\angle{MKL}$ | 3. Given |
| 4. $\angle{MKN}\cong\angle{NKL}$ | 4. Definition of Angle Bisector |
| 5. $\angle{JKM}\cong\angle{NKL}$ | 5. Transitive Property of Congruence |

# Explanation for 28:
## Step1: State given fact
Given
## Step2: Use linear - pair property
Linear Pair (Supplementary) theorem/Postulate
## Step3: Use definition of supplementary angles
Definition of Supplementary Angles
## Step4: State given fact
Given
## Step5: Use vertical - angles congruence
Vertical Angles congruent Theorem
## Step6: Use transitive property of congruence
Transitive Property
## Step7: Use definition of congruent angles
Definition of Congruence
## Step8: Substitute equal - measure angles
Substitution Property
## Step9: Use definition of supplementary angles
Definition of Supplementary Angles

# Answer for 28:
| Statements | Reasons |
|--|--|
| 1. $\angle{1}$ and $\angle{2}$ form a linear pair | 1. Given |
| 2. $\angle{1}$ and $\angle{2}$ are supplementary | 2. Linear Pair (Supplementary) theorem/Postulate |
| 3. $m\angle{1}+m\angle{2}=180^{\circ}$ | 3. Definition of Supplementary Angles |
| 4. $\angle{2}\cong\angle{4}$ | 4. Given |
| 5. $\angle{3}\cong\angle{4}$ | 5. Vertical Angles congruent Theorem |
| 6. $\angle{2}\cong\angle{3}$ | 6. Transitive Property |
| 7. $m\angle{2}=m\angle{3}$ | 7. Definition of Congruence |
| 8. $m\angle{1}+m\angle{3}=180^{\circ}$ | 8. Substitution Property |
| 9. $\angle{1}$ and $\angle{3}$ are supplementary | 9. Definition of Supplementary Angles |

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QUESTION IMAGE

Question

Explanation:

Step1: State given fact

Step2: Apply angle - bisector definition

Step3: State given fact

Step4: Apply angle - bisector definition

Step5: Use transitive property of congruence

Step1: State given fact

Step2: Use linear - pair property

Step3: Use definition of supplementary angles

Step4: State given fact

Step5: Use vertical - angles congruence

Step6: Use transitive property of congruence

Step7: Use definition of congruent angles

Step8: Substitute equal - measure angles

Step9: Use definition of supplementary angles

Answer:

Statements	Reasons
2. $\angle{JKM}\cong\angle{MKN}$	2. Definition of Angle Bisector
3. $\overline{KN}$ bisects $\angle{MKL}$	3. Given
4. $\angle{MKN}\cong\angle{NKL}$	4. Definition of Angle Bisector
5. $\angle{JKM}\cong\angle{NKL}$	5. Transitive Property of Congruence