Arcs and Central Angles

Question 1

What is the central angle of a circle?

Answer 1

The Central angle of a circle is an angle with its vertex at the center of the circle.

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Question 2

What is an arc of a circle?

Answer 2

An arc is an unbroken part of a circle

Question 3

Minor vs Major Arcs

Answer 3

Question 4

What is a semicircle?

Answer 4

A semicircle is an arc formed when endpoints are at the end of a diameter.

***Always use 3 letters to represent a major arc OR a semicircle

Question 5

What is the measure of a minor arc?

What is the measure of a major arc?

Answer 5

The measure of a minor arc: Measure of its central angle

The measure of a major arc: equals 360 - measure of minor arc

Question 6

What is true about the measure of an arc?

Answer 6

The measure of an arc is independent of the size of the circle.

Question 7

What are adjacent arcs of a circle?

Answer 7

Adjacent arcs of a circle

Arcs that have exactly one point in common

Question 8

Arc Addition Postulate

Answer 8

The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs.

Question 9

What are congruent arcs?

Answer 9

Arcs in the same circle or are in congruent arcs that have equal measure

To have congruent arcs they need to be congruent circles and central angle

Question 10

What is Theorem 9-3?

Answer 10

In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.