try this video for extra example 5 and 6 - write a two-column proof.
2) use the reason bank to write a two - column proof for the reflexive property of angles congruence.
given: ∠a
prove: ∠a ≅ ∠a
statements reasons
1. an angle with vertex a exists. 1.
2. m∠a equals the measure of the angle with vertex a. 2.
3. m∠a = m∠a 3.
4. ∠a ≅ ∠a 4.
reasons bank: definition of congruent angles, reflexive property of equality, given, protractor postulate
3) use the reason bank to write a two - column proof for the given situation.
given: (overline{mp}) bisects ∠lmn.
prove: (2(mangle lmp)=mangle lmn)
statements reasons
1. (overline{mp}) bisects ∠lmn. 1.
2. ∠lmp ≅ ∠nmp 2.
3. (mangle lmp = mangle nmp) 3.
4. (mangle lmp + mangle nmp = mangle lmn) 4.
5. (mangle lmp + mangle lmp = mangle lmn) 5.
6. (2(mangle lml)=mangle lmn) 6.
reasons bank: substitution property of equality, angle addition postulate, distribution property of equality, given, definition of congruent angles, definition of angle bisector

Question

Accepted Answer

# Explanation (Problem 2):
## Step1: Match to given premise
Reason: Given
## Step2: Link to protractor postulate
Reason: Protractor Postulate
## Step3: Apply reflexive equality
Reason: Reflexive Property of Equality
## Step4: Use congruent angles definition
Reason: Definition of congruent angles

# Explanation (Problem 3):
## Step1: Match to given premise
Reason: Given
## Step2: Use angle bisector definition
Reason: Definition of angle bisector
## Step3: Use congruent angles definition
Reason: Definition of congruent angles
## Step4: Apply angle addition postulate
Reason: Angle Addition Postulate
## Step5: Use substitution property
Reason: Substitution Property of Equality
## Step6: Apply distribution property
Reason: Distribution Property of Equality

# Answer:
### Completed Proof 2:
| STATEMENTS | REASONS |
|------------|---------|
| 1. An angle with vertex A exists. | 1. Given |
| 2. $m\angle A$ equals the measure of the angle with vertex A. | 2. Protractor Postulate |
| 3. $m\angle A = m\angle A$ | 3. Reflexive Property of Equality |
| 4. $\angle A \cong \angle A$ | 4. Definition of congruent angles |

### Completed Proof 3:
| STATEMENTS | REASONS |
|------------|---------|
| 1. $\overline{MP}$ bisects $\angle LMN$. | 1. Given |
| 2. $\angle LMP \cong \angle NMP$ | 2. Definition of angle bisector |
| 3. $m\angle LMP = m\angle NMP$ | 3. Definition of congruent angles |
| 4. $m\angle LMP + m\angle NMP = m\angle LMN$ | 4. Angle Addition Postulate |
| 5. $m\angle LMP + m\angle LMP = m\angle LMN$ | 5. Substitution Property of Equality |
| 6. $2(m\angle LMP) = m\angle LMN$ | 6. Distribution Property of Equality |

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QUESTION IMAGE

Question

Explanation:

Step1: Match to given premise

Step2: Link to protractor postulate

Step3: Apply reflexive equality

Step4: Use congruent angles definition

Step1: Match to given premise

Step2: Use angle bisector definition

Step3: Use congruent angles definition

Step4: Apply angle addition postulate

Step5: Use substitution property

Step6: Apply distribution property

Answer:

Completed Proof 2:

Completed Proof 3:

STATEMENTS	REASONS
2. $m\angle A$ equals the measure of the angle with vertex A.	2. Protractor Postulate
3. $m\angle A = m\angle A$	3. Reflexive Property of Equality
4. $\angle A \cong \angle A$	4. Definition of congruent angles

STATEMENTS	REASONS
2. $\angle LMP \cong \angle NMP$	2. Definition of angle bisector
3. $m\angle LMP = m\angle NMP$	3. Definition of congruent angles
4. $m\angle LMP + m\angle NMP = m\angle LMN$	4. Angle Addition Postulate
5. $m\angle LMP + m\angle LMP = m\angle LMN$	5. Substitution Property of Equality
6. $2(m\angle LMP) = m\angle LMN$	6. Distribution Property of Equality