In Exercises 27 to 30, fill in the missing reasons for each geometric proof.
Given: 


Prove: 

Exercises 29, 30
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. ? 
Property:
1. The angle bisector is defined as a line or line segment that divides an angle into two equal parts.
2. According to AngleAddition Postulate, if point
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 angle bisector as
Therefore, the second reason is definition of angle bisector.
Now, go from second statement to the third statement.
According to AngleAddition Postulate, the sum of the measures of
Therefore, the third reason for the proof is AngleAddition 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.
Now, go from fourth statement to fifth statement.
Use Substitution Property of Equality and substitute
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