The document defines key concepts related to circles, including arcs, central angles, and types of arcs such as minor, major, and semicircles. It explains how the measures of these arcs relate to their central angles and discusses properties like congruent and adjacent arcs. Additionally, it introduces the concepts of theorems, postulates, and provides an example of the arc addition postulate.

1. CIRCLES

2. Arcs & Central
Angle

3. Definition 11.
An arc is a part of a
circle.

4. Definition 12.
A central angle is an angle
whose vertex is the center of
the circle.

5. Definition 13.
A minor arc (AB) is the union of
points A and B and all the points of
the circle in the interior of central
AOB.
3 TYPES OF ARCS
Note: Minor arc measures less than 180 degrees.
In circle O, the minor arc AB.

6. Definition 14.
A major arc (AQB) is the union of
points A and B and all the points of
the circle in the exterior of central
AOB.
3 TYPES OF ARCS
Note: Major arc measures greater than 180 degrees.
In circle O, the major arc AQB.

7. Definition 15.
A semicircle is the union of the
endpoints of a diameter and all points
of the circle that lie on one side of the
diameter.
3 TYPES OF ARCS
Note: Semicircle measures exactly 180 degrees.
In circle O, the diameter is AC.
Then, the semicircles are arc
ABC and arc AQC.

8. Definition 16.
ARC MEASURE
Minor Arc is equal to the measure of
the central angle.
Major Arc is equal to 360 minus the
measure of the central angle.
Semicircle is equal to 180.

9. Example 1
In circle O, if the central angle is. Then, arc PQ =
Find the following:
a. Minor arc & the measure of each
b. Major arc & the measure of each
c. Semicircle

10. Definition 17.
Congruent arcs are arcs having the
same degree measure
Definition 18.
Adjacent arcs are two arcs on the
same circle that have exactly one
common point.

11. Example 2 Given:
Find:

12. THEOREM & POSTULATE
A theorem is a true statement that can be proven.
A postulate is a statement assumed true even without
proof.
A corollary is a proposition that follows from one already
proved.

13. Postulate 1.
Arc Addition Postulate:
The measure of an arc formed by two
adjacent arcs is the sum of the
measures of the two arcs.
𝑚 ^
𝐴𝐶=𝑚 ^
𝐴𝐵+𝑚 ^
𝐵𝐶

14. Example 3 Find: a.
b.

15. THANK YOU FOR LISTENING!