Geometry /Trigonometry 2
Name: ____________________________ Date: ____________ Block: ______
Notes Sheet
Goal:
At the completion of the lesson, you will be able to…
1) define terms relating to arcs and central angles in circles
2) calculate the measures of arcs and central angles in circles
Purpose: We are studying this material because arcs and central angles are important features of circles. central angle – an angle whose vertex is at the center of a circle arc – segment on the perimeter of a circle with endpoints on the circle measure of an arc – the measure of an arc’s central angle (in degrees) minor arc – an arc formed by two points on a circle whose measure is less than 180°; minor arcs are named by the two endpoints of the arc semicircle – an arc formed by two points on a circle whose measure is equal to 180° major arc – formed by two points on a circle and its measure is greater than 180° major arcs are named with three points: the two endpoints and a point
between them adjacent arcs – arcs that have exactly one point in common (an endpoint) congruent arcs – arcs, in the same circle or in congruent circles, that have equal measures
Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs.
Arc Congruency Theorem
In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.

Geometry /Trigonometry 2
Name: ____________________________ Date: ____________ Block: ______
Practice Problems
1) Using the letters shown in the diagram, name: a.
two central angles _________ _________ b.
a semicircle _________ c.
two minor arcs d.
two major arcs
_________
_________
_________
_________
2) Find the measure of the indicated arc. a.
minor arc AB = _______ b.
minor arc AC = _______ c.
major arc ABD = _______ d.
major arc BAD = _______ e.
major arc CDA = _______ f.
major arc CDB = _______
3) Find the measure of the indicated angle or arc. a.

GQF

_______ b.

EQF

_______ c.

GQE

_______ d.
minor arc GE = _______ e.
major arc GHE = _______ f.
major arc EHF = _______