Name: ________________________ Class: ___________________ Date: __________
ID: A
11.2 Chords & Central Angles Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. In the diagram below, circle O has a radius of 5, and CE = 2. Diameter AC is perpendicular to chord BD at
E.
What is the length of BD ?
a. 12
b. 10
____
c.
d.
8
4
2. The circle graph shows the colors of automobiles sold at a car dealership. Find mCD.
a.
mCD = 36°
c.
mCD = 170°
b.
mCD = 10°
d.
mCD = 20°
1
Name: ________________________
____
____
ID: A
3. Find mCFB.
a.
mCFB = 130°
c.
mCFB = 230°
b.
mCFB = 140°
d.
mCFB = 90°
4. WX ≅ YZ . Find mWX .
a.
mWX = 17°
c.
mWX = 1°
b.
mWX = 5°
d.
mWX = 23°
2
ID: A
11.2 Chords & Central Angles Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: C
Because OC is a radius, its length is 5. Since CE = 2 OE = 3.
BD = 8 .
PTS: 2
2. ANS: A
mCD = m∠CPD
mCD = 0.10(360°)
REF: fall0811ge
STA: G.G.49
EDO is a 3-4-5 triangle. If ED = 4,
TOP: Chords
Theorem: The measure of a minor arc is equal to the measure
of its central angle.
m∠CPD is 10% of 360°.
mCD = 36°
Feedback
A
B
C
D
Correct!
The measure of a minor arc is equal to the measure of its central angle.
The measure of a minor arc is equal to the measure of its central angle.
The measure of a minor arc is equal to the measure of its central angle.
PTS:
OBJ:
TOP:
DOK:
1
DIF: Average
11-2.1 Application
11-2 Arcs and Chords
DOK 2
REF: 1cd5521a-4683-11df-9c7d-001185f0d2ea
LOC: MTH.C.11.03.05.03.02.006
KEY: arc measure | circle graph | central angle
1
ID: A
3. ANS: A
m∠BPD = 50°
mBD = 50°
m∠CPF = m∠FPD = 90°
mCF = mFD = 90°
m∠FPD = m∠FPB + m∠BPD
90° = m∠FPB + 50°
m∠FPD = 40°
Vertical Angle Theorem
m∠BPD = 50°
Definition of perpendicular lines
m∠CPF = m∠FPD = 90°
mFB = 40°
Angle Addition Postulate
Substitute.
Simplify.
m∠FPD = 40°
mCFB = mCF + mFB
Arc Addition Postulate
mCFB = 90° + 40° = 130°
Substitute.
Feedback
A
B
C
D
Correct!
Add the measure of arc CF and the measure of arc FB.
Add the measure of arc CF and the measure of arc FB.
Add the measure of arc CF and the measure of arc FB.
PTS:
OBJ:
TOP:
DOK:
4. ANS:
1
DIF: Average
REF: 1cd5792a-4683-11df-9c7d-001185f0d2ea
11-2.2 Using the Arc Addition Postulate
LOC: MTH.C.11.03.05.03.02.005
11-2 Arcs and Chords
KEY: arc measure | arc addition postulate
DOK 2
A
Congruent chords have congruent arcs.
mWX = mYZ
3x + 2 = 4x − 3
Substitute the given measures.
2= x−3
Subtract 3x from both sides.
5=x
Add 3 to both sides.
Substitute 5 for x and simplify.
mWX = 3(5) + 2 = 17°
Feedback
A
B
C
D
Correct!
This is x. Now solve for the arc length.
Set the two expressions equal to each other and solve.
Congruent chords have congruent arcs.
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Average
REF: 1cd7b476-4683-11df-9c7d-001185f0d2ea
11-2.3 Applying Congruent Angles, Arcs, and Chords
NY.NYLES.MTH.05.GEO.G.G.49.a
MTH.C.11.03.05.03.02.006 | MTH.C.11.03.05.04.005
TOP: 11-2 Arcs and Chords
chord | arc measure
DOK: DOK 2
2
Name: ________________________ Class: ___________________ Date: __________
ID: B
11.2 Chords & Central Angles Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. WX ≅ YZ . Find mWX .
a.
mWX = 5°
c.
mWX = 17°
b.
mWX = 23°
d.
mWX = 1°
2. In the diagram below, circle O has a radius of 5, and CE = 2. Diameter AC is perpendicular to chord BD at
E.
What is the length of BD ?
a. 10
b. 12
c.
d.
1
4
8
Name: ________________________
____
____
ID: B
3. The circle graph shows the colors of automobiles sold at a car dealership. Find mCD.
a.
mCD = 170°
c.
mCD = 10°
b.
mCD = 20°
d.
mCD = 36°
4. Find mCFB.
a.
mCFB = 140°
c.
mCFB = 90°
b.
mCFB = 130°
d.
mCFB = 230°
2
ID: B
11.2 Chords & Central Angles Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: C
Congruent chords have congruent arcs.
mWX = mYZ
3x + 2 = 4x − 3
2= x−3
5=x
mWX = 3(5) + 2 = 17°
Substitute the given measures.
Subtract 3x from both sides.
Add 3 to both sides.
Substitute 5 for x and simplify.
Feedback
A
B
C
D
This is x. Now solve for the arc length.
Congruent chords have congruent arcs.
Correct!
Set the two expressions equal to each other and solve.
PTS: 1
DIF: Average
REF: 1cd7b476-4683-11df-9c7d-001185f0d2ea
OBJ: 11-2.3 Applying Congruent Angles, Arcs, and Chords
STA: NY.NYLES.MTH.05.GEO.G.G.49.a
LOC: MTH.C.11.03.05.03.02.006 | MTH.C.11.03.05.04.005
TOP: 11-2 Arcs and Chords
KEY: chord | arc measure
DOK: DOK 2
2. ANS: D
Because OC is a radius, its length is 5. Since CE = 2 OE = 3. EDO is a 3-4-5 triangle. If ED = 4,
BD = 8 .
PTS: 2
REF: fall0811ge
STA: G.G.49
1
TOP: Chords
ID: B
3. ANS: D
mCD = m∠CPD
mCD = 0.10(360°)
Theorem: The measure of a minor arc is equal to the measure
of its central angle.
m∠CPD is 10% of 360°.
mCD = 36°
Feedback
A
B
C
D
The measure of a minor arc is equal to the measure of its central angle.
The measure of a minor arc is equal to the measure of its central angle.
The measure of a minor arc is equal to the measure of its central angle.
Correct!
PTS: 1
DIF: Average
OBJ: 11-2.1 Application
TOP: 11-2 Arcs and Chords
DOK: DOK 2
4. ANS: B
m∠BPD = 50°
mBD = 50°
m∠CPF = m∠FPD = 90°
mCF = mFD = 90°
m∠FPD = m∠FPB + m∠BPD
90° = m∠FPB + 50°
m∠FPD = 40°
REF: 1cd5521a-4683-11df-9c7d-001185f0d2ea
LOC: MTH.C.11.03.05.03.02.006
KEY: arc measure | circle graph | central angle
Vertical Angle Theorem
m∠BPD = 50°
Definition of perpendicular lines
m∠CPF = m∠FPD = 90°
mFB = 40°
Angle Addition Postulate
Substitute.
Simplify.
m∠FPD = 40°
mCFB = mCF + mFB
Arc Addition Postulate
mCFB = 90° + 40° = 130°
Substitute.
Feedback
A
B
C
D
Add the measure of arc CF and the measure of arc FB.
Correct!
Add the measure of arc CF and the measure of arc FB.
Add the measure of arc CF and the measure of arc FB.
PTS:
OBJ:
TOP:
DOK:
1
DIF: Average
REF: 1cd5792a-4683-11df-9c7d-001185f0d2ea
11-2.2 Using the Arc Addition Postulate
LOC: MTH.C.11.03.05.03.02.005
11-2 Arcs and Chords
KEY: arc measure | arc addition postulate
DOK 2
2
Name: ________________________ Class: ___________________ Date: __________
11.2 Chords & Central Angles Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. The circle graph shows the colors of automobiles sold at a car dealership. Find mCD.
a.
mCD = 20°
c.
mCD = 10°
b.
mCD = 36°
d.
mCD = 170°
2. WX ≅ YZ . Find mWX .
a.
mWX = 23°
c.
mWX = 17°
b.
mWX = 1°
d.
mWX = 5°
1
ID: C
Name: ________________________
____
____
ID: C
3. Find mCFB.
a.
mCFB = 130°
c.
mCFB = 90°
b.
mCFB = 140°
d.
mCFB = 230°
4. In the diagram below, circle O has a radius of 5, and CE = 2. Diameter AC is perpendicular to chord BD at
E.
What is the length of BD ?
a. 4
b. 10
c.
d.
2
8
12
ID: C
11.2 Chords & Central Angles Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: B
mCD = m∠CPD
mCD = 0.10(360°)
Theorem: The measure of a minor arc is equal to the measure
of its central angle.
m∠CPD is 10% of 360°.
mCD = 36°
Feedback
A
B
C
D
The measure of a minor arc is equal to the measure of its central angle.
Correct!
The measure of a minor arc is equal to the measure of its central angle.
The measure of a minor arc is equal to the measure of its central angle.
PTS:
OBJ:
TOP:
DOK:
2. ANS:
1
DIF: Average
REF: 1cd5521a-4683-11df-9c7d-001185f0d2ea
11-2.1 Application
LOC: MTH.C.11.03.05.03.02.006
11-2 Arcs and Chords
KEY: arc measure | circle graph | central angle
DOK 2
C
Congruent chords have congruent arcs.
mWX = mYZ
3x + 2 = 4x − 3
Substitute the given measures.
2= x−3
Subtract 3x from both sides.
5=x
Add 3 to both sides.
Substitute 5 for x and simplify.
mWX = 3(5) + 2 = 17°
Feedback
A
B
C
D
Congruent chords have congruent arcs.
Set the two expressions equal to each other and solve.
Correct!
This is x. Now solve for the arc length.
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Average
REF: 1cd7b476-4683-11df-9c7d-001185f0d2ea
11-2.3 Applying Congruent Angles, Arcs, and Chords
NY.NYLES.MTH.05.GEO.G.G.49.a
MTH.C.11.03.05.03.02.006 | MTH.C.11.03.05.04.005
TOP: 11-2 Arcs and Chords
chord | arc measure
DOK: DOK 2
1
ID: C
3. ANS: A
m∠BPD = 50°
mBD = 50°
m∠CPF = m∠FPD = 90°
mCF = mFD = 90°
m∠FPD = m∠FPB + m∠BPD
90° = m∠FPB + 50°
m∠FPD = 40°
Vertical Angle Theorem
m∠BPD = 50°
Definition of perpendicular lines
m∠CPF = m∠FPD = 90°
mFB = 40°
Angle Addition Postulate
Substitute.
Simplify.
m∠FPD = 40°
mCFB = mCF + mFB
Arc Addition Postulate
mCFB = 90° + 40° = 130°
Substitute.
Feedback
A
B
C
D
Correct!
Add the measure of arc CF and the measure of arc FB.
Add the measure of arc CF and the measure of arc FB.
Add the measure of arc CF and the measure of arc FB.
PTS: 1
DIF: Average
REF: 1cd5792a-4683-11df-9c7d-001185f0d2ea
OBJ: 11-2.2 Using the Arc Addition Postulate
LOC: MTH.C.11.03.05.03.02.005
TOP: 11-2 Arcs and Chords
KEY: arc measure | arc addition postulate
DOK: DOK 2
4. ANS: C
Because OC is a radius, its length is 5. Since CE = 2 OE = 3. EDO is a 3-4-5 triangle. If ED = 4,
BD = 8 .
PTS: 2
REF: fall0811ge
STA: G.G.49
2
TOP: Chords