use this diagram for items 5 - 8.
5. write a statement from the diagram that can be justified by using the angle addition postulate.
6. write a statement from the diagram that can be justified by using the definition of a right angle.
7. given that ( k ) is the midpoint of ( overline{f j} ), write a statement that can be justified by using the definition of a midpoint.
8. given that ( angle g h f cong angle j f h ), write a statement that can be justified by using the definition of congruent angles.
lesson 6 - 2
9. complete the proof.
given: ( x y = 6, x z = 14 )
prove: ( y z = 8 )
10. based on the given information in item 9, can you conclude that ( y ) is the midpoint of ( overline{x z} )? explain your reasoning.

Question

Accepted Answer

### Item 9
# Explanation:
## Step 1: Identify the Reason for Statement 1
The first statement $ XY = 6, XZ = 14 $ is given, so the reason is "Given".
## Step 2: Identify the Reason for Statement 2
The equation $ XY + YZ = XZ $ is based on the Segment Addition Postulate, which states that if a point $ Y $ is between $ X $ and $ Z $, then $ XY + YZ = XZ $. So the reason is "Segment Addition Postulate".
## Step 3: Identify the Reason for Statement 3
We substitute $ XY = 6 $ and $ XZ = 14 $ into the equation $ XY + YZ = XZ $, so this is "Substitution Property (substituting $ XY = 6 $ and $ XZ = 14 $ into $ XY + YZ = XZ $)".
## Step 4: Identify the Reason for Statement 4
To solve $ 6 + YZ = 14 $ for $ YZ $, we use the Subtraction Property of Equality (subtract 6 from both sides: $ YZ=14 - 6=8 $). So the reason is "Subtraction Property of Equality".

# Answer:
| Statements | Reasons |
| --- | --- |
| 1. $ XY = 6, XZ = 14 $ | 1. Given |
| 2. $ XY + YZ = XZ $ | 2. Segment Addition Postulate |
| 3. $ 6 + YZ = 14 $ | 3. Substitution Property (substituting $ XY = 6 $ and $ XZ = 14 $ into $ XY + YZ = XZ $) |
| 4. $ YZ = 8 $ | 4. Subtraction Property of Equality |

### Item 10
# Brief Explanations:
To determine if $ Y $ is the midpoint of $ \overline{XZ} $, we need to check if $ XY = YZ $. From Item 9, we know $ XY = 6 $ and $ YZ = 8 $. Since $ 6
eq8 $, $ XY
eq YZ $. A midpoint of a segment divides the segment into two equal - length segments. So, if $ Y $ were the midpoint, $ XY $ and $ YZ $ would have to be equal, but they are not.
# Answer:
No, we cannot conclude that $ Y $ is the midpoint of $ \overline{XZ} $. A midpoint of a segment divides the segment into two segments of equal length. We found that $ XY = 6 $ and $ YZ = 8 $, and since $ 6
eq8 $, $ XY
eq YZ $, so $ Y $ does not divide $ \overline{XZ} $ into two equal - length segments.

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QUESTION IMAGE

Question

Explanation:

Item 9

Step 1: Identify the Reason for Statement 1

Step 2: Identify the Reason for Statement 2

Step 3: Identify the Reason for Statement 3

Step 4: Identify the Reason for Statement 4

Answer:

Item 10

Statements	Reasons
2. \( XY + YZ = XZ \)	2. Segment Addition Postulate
3. \( 6 + YZ = 14 \)	3. Substitution Property (substituting \( XY = 6 \) and \( XZ = 14 \) into \( XY + YZ = XZ \))
4. \( YZ = 8 \)	4. Subtraction Property of Equality