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 Prop. 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:
Step1:
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.congruent angles have equal measure 
Step2:
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
Elementary Geometry For College Students, 7e
Precalculus: Mathematics for Calculus (Standalone Book)
Elementary Technical Mathematics
Calculus (MindTap Course List)
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Multivariable Calculus
Single Variable Calculus: Early Transcendentals, Volume I
Mathematical Excursions (MindTap Course List)
Calculus of a Single Variable
Probability and Statistics for Engineering and the Sciences
Finite Mathematics for the Managerial, Life, and Social Sciences
Single Variable Calculus: Early Transcendentals
Intermediate Algebra
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus: Early Transcendentals
Elements Of Modern Algebra
Statistics for The Behavioral Sciences (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Applied Calculus
Understanding Basic Statistics
Mathematical Applications for the Management, Life, and Social Sciences
Calculus: Early Transcendental Functions
Essentials Of Statistics
Finite Mathematics
Trigonometry (MindTap Course List)
Contemporary Mathematics for Business & Consumers
Calculus: Early Transcendental Functions (MindTap Course List)
Single Variable Calculus
Calculus: An Applied Approach (MindTap Course List)
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
Introduction To Statistics And Data Analysis
Multivariable Calculus
Research Methods for the Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
College Algebra (MindTap Course List)
STATISTICS F/BUSINESS+ECONOMICSTEXT
Mathematics For Machine Technology
Statistics for Business & Economics, Revised (MindTap Course List)
Research Methods for the Behavioral Sciences (MindTap Course List)