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


Prove: 



To prove: The
Given: The diameters
Postulate used:
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:
We need prove that if
PROOF  
Statements  Reasons 
1. 
1. Given 
Step 2:
The diameters
Since, vertical angles are congruent.
Therefore, the angles are congruent, then
PROOF  
Statements  Reasons 
1. 
1. Given 
2. 
2. vertical angles are congruent. 
3. 
3. congruent angles have equal measures. 
Step 3:
Since,
Therefore, the measures degree of a central angle is equal to the degree measure of its intercepted arc.
Thus,
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