supply the missing statements and reasons in the following two - column proof.
given: ( overline{cb}congoverline{yz} )
prove: ( overline{cy}congoverline{bz} )
1. ( overline{cb}congoverline{yz} ) 1. given
2. 2. definition of congruent segments
3. 3. addition property of equality
4. ( cb + by = cy;by + yz = bz ) 4.
5. 5.
6. ( overline{cy}congoverline{bz} ) 6.

Question

Accepted Answer

# Explanation:
## Step1: Write the definition of congruent segments
$$CB = YZ$$
## Step2: Add $BY$ to both sides
$$CB + BY=YZ + BY$$
## Step3: State the Segment Addition Postulate
Segment Addition Postulate
## Step4: Substitute using the equations from Step 3
$$CY = BZ$$
## Step5: Write the definition of congruent segments
Definition of congruent segments

# Answer:
| Statements | Reasons |
|--|--|
| 1. $\overline{CB}\cong\overline{YZ}$ | 1. given |
| 2. $CB = YZ$ | 2. definition of congruent segments |
| 3. $CB + BY=YZ + BY$ | 3. Addition Property of Equality |
| 4. $CB + BY = CY;BY + YZ = BZ$ | 4. Segment Addition Postulate |
| 5. $CY = BZ$ | 5. Substitution (from Steps 3 and 4) |
| 6. $\overline{CY}\cong\overline{BZ}$ | 6. definition of congruent segments |

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QUESTION IMAGE

Question

Explanation:

Step1: Write the definition of congruent segments

Step2: Add \(BY\) to both sides

Step3: State the Segment Addition Postulate

Step4: Substitute using the equations from Step 3

Step5: Write the definition of congruent segments

Answer:

Statements	Reasons
2. \(CB = YZ\)	2. definition of congruent segments
3. \(CB + BY=YZ + BY\)	3. Addition Property of Equality
4. \(CB + BY = CY;BY + YZ = BZ\)	4. Segment Addition Postulate
5. \(CY = BZ\)	5. Substitution (from Steps 3 and 4)
6. \(\overline{CY}\cong\overline{BZ}\)	6. definition of congruent segments