In Exercises 30 and 31, complete each proof.
Given: 

Prove: 

PROOF  
Statements  Reasons 
1.

1. Given 
2.

2.

3.

3.

4.

4.

5.

5.

6.

6.

7.

7. Multiplication Property of Equality 
To prove: The
Given: The
Postulate used:
The measure of an inscribed angle is onehalf the measure of its intercepted arc.
Central angle postulate:
In a circle, the degree of a central angle is equal to the degree measure of its intercepted arc.
Definition:
In a circle or congruent circles, congruent arcs are arcs with equal measures.
Proof:
Step 1:
Since,
Now,
Thus, alternate interior angles are congruent.
Since, congruent angles have equal measures.
Thus,
PROOF  
Statements  Reasons 
1. 
1. Given 
2. 
2. Alternate interior angle 
3. 
3.congurent angles have equal measure 
Step 2:
Since,
Therefore, the measure of an inscribed angle is equal to the onehalf the measure of an inscribed arc.
Thus,
Also, the measure of a central angle is equal to the measure of its intercepted arc.
Thus,
Now, by substitution, using statements 3 and 5 we obtain
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