Geometry Honors Section 9.1 Segments and Arcs of Circles

1. Geometry Honors Section 9.1Segments and Arcs of Circles

2. A *circle is a set of points, in a plane, that are equidistant from a given point.This given point is called the _______ of the circle. center

3. A circle can be named by using the symbol _____and naming the center of the circle. The circle to the right is__________.

4. A *radius (plural: radii) is a segment from the center to a point on the circle.

5. A *chordis a segment whose endpoints are on the circle.

6. A *diameter is a chord which contains the center of the circle.

7. An arcis an unbroken part of a circle.Any two distinct points on a circle divide the circle into two arcs.The two points are called the _________of the arc. endpoints

8. If the two points are the endpoints of a diameter, then each of the two arcs formed is called a __________A semicircle is named by its two endpoints and another point that lies on the arc.Example: Name twosemicircles._____ & _____ semicircle.

9. If the two points are not the endpoints of a diameter, then a minor arc and a major arc are formed.

10. A *minor arc is an arc which is shorter than a semicircle.A minor arc is named by its two endpoints.Example: Name two minor arcs._____ & _____

11. A *major arc is an arc which is longer than a semicircle. A major arc is named by its two endpoints and another point that lies on the arc..Example: Name twomajor arcs._______ & _______

12. A *central angle of a circle is an angle whose vertex is at the center and whose sides are radii.The arc between the outer endpoints of the two radii is called the __________ arc of the central angle. intercepted

13. The degree measure of a minor arc is equal to the measure of its central angle. The degree measure of a major arc is equal to 360⁰ - the measure of the associated minor arc.The degree measure of a semicircle is ______. 180⁰

14. When referring to the measure of an arc, use the notation __________

15. 100⁰ 38⁰

16. The following theorem mentions congruent circles. Two circles are congruent ifftheir radii are congruent.Chords and Arcs Theorem In a circle (or in congruent circles), two chords are congruent iff the minor arcs they determine are congruent.

18. Radius and Chord TheoremIf a radius is perpendicular to a chord, then the radius bisects the chord and its arc.