Download 10.2 Homework - Haiku Learning

Name: ___________________________________________
10.2 Notes ~ Arcs and Chords
Date: ____________________________
Geometry Advanced
Objectives:
1) Find the measures of arcs and central angles.
Central Angle: In a plane, an angle whose vertex is at the center of a circle.
Minor Arc: An arc whose central angle measures less than 180o.
Major Arc: An arc whose central angle measures greater than 180 o. You must use
3 letters to name a major arc.
Semicircle: Endpoints of the arc are endpoints of a diameter. The arc measures
exactly 180o.
Postulate 26 ~ Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the 2 arcs.
Example 1
Find the measure of each arc of T


A. m GF

E. m HGF

B. m GHF

C. m GD


F. m HDG

D. m HD
G. m HFG

H. m GH
 Two arcs of the same circle or of XYZ congruent circles are congruent if they have the same measure.
 Two minor arcs of the same circle or of congruent circles are congruent if their central angles are
congruent.

 
 A point Y is called the midpoint of XYZ if XY  YZ . Any line, segment or ray that contains Y
bisects XYZ

Find m AD given D is the midpoint of
Example 2
A.

ADC
Example 3
Are
and
congruent? Explain.
10.2 HOMEWORK
MQ and NR are diameters. Find the indicated measure.
Then determine whether the arc is a major arc, a minor arc, or a semicircle.
1.
Measure
Type of Arc
Measure
2.
3.
Type of Arc
4.
5.
6.
7.
8.
9.
10.
C is the center of the circle. Find all possible values of x.
11.
12.


13.

14. m PN is 45o less than twice m NM . Find m NM .
Answers: 1) 63o, Minor
2) 117o, Minor
3) 180o, semicircle
7) 297o, major,
8) 35o, minor
9) 278o, major
10) 297o, major
4) 215o, major
11) 12
5) 63o, minor
12) 73
6) 117o, minor
13) 13
14) 90