SECTION+9.1+CHORDS+AND+ARCS

Objectives: 1. Define a circle and its associated parts, and use them in constructions. 2. Define and use the degree measure of arcs. 3. Define and use the length measure of arcs. 4. Prove a theorem about chords and their intercepted arcs.


 * __DEFINITIONS AND BLUE BOXES!!__**

CIRCLE- A circle is a set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle. RADIUS- Is a segment from the center of the circle to a point on the circle. CHORD- Is a segment whose endpoints line on the circle. DIAMETER- Is a chord that contains the center of the circle. ARC- Is an unbroken part of a circle. ENDPOINTS- The two distinct points on the circle that divide the circle into two arcs. SEMICIRCLE- Is a arc whose endpoints are endpoints of a diameter. Sometimes it is called a HALF-CIRCLE. MINOR ARC- Is an arc that is shorter than a simicircle of that circle. It is named by its endpoints. MAJOR ARC- Is an arc that is no longer than a semicircle of that circle. CENTRAL ANGLE- Is an angle in the plane of a circle whose vertex is the center of the circle. INTERCEPTED ARC- An arc whose whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle. DEGREE MEASURE OF ARCS- *The degree measure of a minor arc is tha measure of its central angle.
 * The degree measure of a major arcis 360 degrees minus the degrre measure of its minor arc.
 * The degree measure of a semicircle is 180 degrees.

ARC LENGTH- If r is the radius of a circle and M is the degree measure of an arc of the circle, then the length, L, of the arc is given by the following: L = M/360 degrees(2 pie r) CHORDS AND ARCS THEOREM- In a circle, or in congruent circles, the arcs of congruent chords are __congruent.__ THE CONVERSE OF THE CHORDS AND ARCS THEOREM- In a circle or in congruent circles, the chords of congruent arcs are __congruent.__

__EXAMPLE:__