11.1.2 Arcs and Chords

Question 1

central angle

Answer 1

an angle whose vertex is the center of a circle

Question 2

arc

Answer 2

an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them

Question 3

minor arc

Answer 3

an arc whose points are on or in the interior of a central angle

Question 4

major arc

Answer 4

an arc whose points are on or in the exterior of a central angle

Question 5

endpoints of an arc

Answer 5

lie on a diameter, the arc is a semicircle

Question 6

adjacent arcs

Answer 6

the arcs of the same circle that intersect at exactly one point

Question 7

congruent arcs

Answer 7

within a circle or congruent circles, they are two arcs that have the same measure

Question 8

Arc Addition Postulate

Answer 8

The measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs.

Question 9

Theorem In a circle or congruent circles

Answer 9

(1) Congruent central angles have congruent chords.
(2) Congruent chords have congruent arcs.
(3) Congruent arcs have congruent central angles.

Question 10

Theorem In a circle

Answer 10

if a radius (or diameter) is perpendicular to a chord, then it bisects the chord and its arc.

Question 11

Theorem In a circle

Answer 11

the perpendicular bisector of a chord is a radius (or diameter)