In Exercises 27 to 30, fill in the missing reasons for each geometric proof.
Given: E is the midpoint of
Prove:
Exercises 27, 28
PROOF  
Statements  Reasons 
1.

1. ? 
2.

2. ? 
3.

3. ? 
4.

4. ? 
5.

5. ? 
6.

6. ? 
To find:
The missing reasons for the geometric proof.
Given:
The given table is shown below.
PROOF  
Statements  Reasons 
1. 
1. ? 
2. 
2. ? 
3. 
3. ? 
4. 
4. ? 
5. 
5. ? 
6. 
6. ? 
Approach:
1. Midpoint on a line is defined as the point which divides the line into two segments of equal length.
2. According to SegmentAddition Postulate, if two points
3. According to Substitution Property of Equality, if
4. The Multiplication Property of Equality states that if both the sides of an equation is multiplied by a same number then the sides of the equation remains equal.
Calculation:
The first statement of the proof is given below.
Therefore, the first reason of the proof is given.
Now, go from first statement to the second statement.
Use Definition of Midpoint as
Therefore, the second reason is Definition of Midpoint.
Now, go from second statement to the third statement.
Use SegmentAddition Postulate as
Therefore, the third reason is SegmentAddition Postulate.
Now, go from third statement to fourth statement.
Use Substitution Property of Equality and substitute
Therefore, the fourth reason for the proof is Substitution Property of Equality
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