Geometry Honors Section 9.1 Segments and Arcs of Circles

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

A circle can be named by using the symbol _____ and naming the center of the circle. The circle to the right is __________.

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

A *chord is a segment whose endpoints are on the circle.

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

An arc is an unbroken part of a circle An arc is 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

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 two semicircles. _____ & _____ semicircle.

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

A. minor arc is an arc which is shorter than a semicircle 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. _____ & _____

A. major arc is an arc which is longer than a semicircle 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 two major arcs. _______ & _______

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

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

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

100⁰ 38⁰

The following theorem mentions congruent circles The following theorem mentions congruent circles. Two circles are congruent iff their 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.

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