Geometry Section 10.2 Arcs & Chords

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. 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 smaller than a semicircle A *minor arc is an arc which is smaller than a semicircle. A minor arc is named by its two endpoints. Name two minor arcs. ____ & ____

A. major arc is an arc which is larger than a semicircle A *major arc is an arc which is larger than a semicircle. A major arc is named by its two endpoints and another point that lies on the arc. Name two major arcs. ______ & ______

A *central angle of a circle is an angle whose vertex is at the center of the circle. 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 minus the measure of the associated minor arc.

The degree measure of a semicircle is ______.

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

Postulate 26: Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. For the figure at the top of the page, ______________

The following definition and theorem both mention congruent circles The following definition and theorem both mention congruent circles. Two circles are congruent iff their radii are congruent.

Two arcs are congruent iff they lie in congruent circles and they have the same measure.

Theorem 10.4 Chords and Arcs Theorem   In a circle (or in congruent circles), two chords are congruent iff the arcs determined by their endpoints are congruent.