Section 10.2 Arcs and Chords

Vocabulary Central Angle – An angle whose vertex is at the center of the circle. Minor Arc – An arc that is less than half of a circle. Minor arcs are named with 2 letters. Major Arc – An arc that is greater than half of a circle. Major arcs are named with 3 letters. Semi-circle – an arc that is exactly half of a circle. Semicircles are named with 3 letters.

Measuring Arcs Arcs are measured in degrees. The measurement of an arc is equal to the measurement of its central angle. Arc Addition Postulate Two smaller arcs can be added together to form a longer arc.

Example

Congruent Arcs Theorem Two minor arcs are congruent if and only if their corresponding chords are congruent.

Chord-Diameter Theorems If a diameter of a circle is perpendicular to a chord, then it bisects the chord and its arcs. If one chord is the perpendicular bisector of a second chord, then the first chord is a diameter.

Congruent Chord Theorem Two chords are congruent if and only if they are equidistant from the center of the circle.

Example

Example

Homework Pg 607 #12-34, 36-38, 42-47