Arcs Chords and Central Angles
Key Vocabulary
Diagram
Mathematical Symbols
A minor arc is equal to the
measure of its central angle.
mDE  mDCE  x
A major arc is equal to 360°
minus the measure of its
central angle.
mDFE  360°  mDCE
 360°  x°
The measure of an arc formed
by two adjacent arcs is the
sum of the measures of the two
arcs.
mABC  mAB  mBC
Congruent central angles
have congruent chords.
RQ  YZ
Congruent chords have
congruent arcs.
RQ  YZ
Congruent arcs have
congruent central angles.
QXR  ZXY
Check for Understanding Part 1
1. The measure of a central angle is 60°. What is the measure
of its minor arc?
__________________
2. What will be the sum of a central angle’s minor arc
and major arc?
__________________
3. Congruent __________________ have congruent chords.
Use circle A to find each measure.
4. mDE
5. mCBE
6. mEBD
7. mCBD
8. mCAB
9. mCD
Arcs and Their Measure
• A central angle is an angle whose vertex is the center of a circle.
• An arc is an unbroken part of a circle consisting of two points on a circle and all the points
on the circle between them.
ABC is a
central angle.
is a major arc.
 360°  mABC
 360°  93°
 267°
is a minor arc
 mABC  93°.
• If the endpoints of an arc lie on a diameter, the arc is a semicircle and its measure is 180°.
Arc Addition Postulate
The measure of an arc formed by two adjacent arcs
is the sum of the measures of the two arcs.
m ABC  m AB  mBC
Check for Understanding Part 2
Find each measure.
1. mHJ
3. mCDE
2. mFGH
4. mBCD
5. mLMN
6. mLNP
Congruent arcs are arcs that have the same measure.
Congruent Arcs, Chords, and Central Angles
If mBEA  mCED,
then BA  CD.
Congruent central angles have
congruent chords.
If BA  CD , then
BA  CD.
Congruent chords have
congruent arcs.
In a circle, if a radius or diameter is perpendicular
to a chord, then it bisects the chord and its arc.
If BA  CD , then
mBEA  mCED.
Congruent arcs have
congruent central angles.
Since AB  CD, AB
bisects CD and CD.
Find each measure.
7. QR  ST . Find mQR .
8. HLG  KLJ. Find GH.
Find each length to the nearest tenth.
9. NP
10. EF
Solutions
Check for
Understanding Part 1
Check for
Understanding Part 2
1.60°
2. 360°
1.63°
2. 117°
3.central angles
4. 32°
3. 130°
4. 140°
5.263°
6. 328°
5. 75°
6. 225°
7.295°
9. 65°
8. 32°
7. 88°
8. 21
9. 16.0
10. 30.0