Five-Minute Check (over Lesson 10–1)
CCSS
Then/Now
New Vocabulary
Key Concept: Sum of Central Angles
Example 1: Find Measures of Central Angles
Key Concept: Arcs and Arc Measure
Example 2: Classify Arcs and Find Arc Measures
Theorem 10.1
Example 3: Real-World Example: Find Arc Measures in Circle Graphs
Postulate 10.1: Arc Addition Postulate
Example 4: Use Arc Addition to Find Measures of Arcs
Key Concept: Arc Length
Example 5: Find Arc Length
Over Lesson 10–1
Name a radius.
A.
B.
C.
D.
Over Lesson 10–1
Name a radius.
A.
B.
C.
D.
Over Lesson 10–1
Name a chord.
___
A. LF
___
B. MF
___
C. OM
___
D. NF
Over Lesson 10–1
Name a chord.
___
A. LF
___
B. MF
___
C. OM
___
D. NF
Over Lesson 10–1
Name a diameter.
____
A. OM
___
B. OL
___
C. NF
____
D. MF
Over Lesson 10–1
Name a diameter.
____
A. OM
___
B. OL
___
C. NF
____
D. MF
Over Lesson 10–1
Refer to the figure. Find BC.
A. 2
B. 3
C. 4
D. 5
Over Lesson 10–1
Refer to the figure. Find BC.
A. 2
B. 3
C. 4
D. 5
Over Lesson 10–1
Refer to the figure. Find DE.
A. 9
B. 11
C. 13
D. 15
Over Lesson 10–1
Refer to the figure. Find DE.
A. 9
B. 11
C. 13
D. 15
Over Lesson 10–1
Find the length of the radius of the circle.
A. 6.5 in.
B. 10.9 in.
C. 13 in.
D. 17 in.
Over Lesson 10–1
Find the length of the radius of the circle.
A. 6.5 in.
B. 10.9 in.
C. 13 in.
D. 17 in.
Content Standards
G.C.2 Identify and describe relationships among
inscribed angles, radii, and chords.
G.C.5 Derive using similarity the fact that the length
of the arc intercepted by an angle is proportional to
the radius, and define the radian measure of the
angle as the constant of proportionality; derive the
formula for the area of a sector.
Mathematical Practices
6 Attend to precision.
4 Model with mathematics.
You measured angles and identified congruent
angles.
• Identify central angles, major arcs, minor
arcs, and semicircles, and find their
measures.
• Find arc lengths.
• central angle
• arc
• minor arc
• major arc
• semicircle
• congruent arcs
• adjacent arcs
• arc length
Find Measures of Central Angles
Find the value of x.
Find Measures of Central Angles
The sum of the measures of
Substitution
Simplify.
Add 2 to each side.
Divide each side
by 26.
Answer:
Find Measures of Central Angles
The sum of the measures of
Substitution
Simplify.
Add 2 to each side.
Divide each side
by 26.
Answer: x = 7
Find the value of x.
A. 9
B. 10
C. 11
D. 65
Find the value of x.
A. 9
B. 10
C. 11
D. 65
Classify Arcs and Find Arc Measures
Answer:
Classify Arcs and Find Arc Measures
Answer:
Classify Arcs and Find Arc Measures
Classify Arcs and Find Arc Measures
Answer:
Classify Arcs and Find Arc Measures
Answer:
Classify Arcs and Find Arc Measures
Answer:
Classify Arcs and Find Arc Measures
Answer:
A.
B.
C.
D.
A.
B.
C.
D.
A.
B.
C.
D.
A.
B.
C.
D.
A.
B.
C.
D.
A.
B.
C.
D.
Find Arc Measures in Circle
Graphs
mLPK = 0.21(360)
= 75.6
Answer:
Find 21% of 360.
Simplify.
Find Arc Measures in Circle
Graphs
mLPK = 0.21(360)
= 75.6
Answer:
Find 21% of 360.
Simplify.
Find Arc Measures in Circle
Graphs
Find Arc Measures in Circle
Graphs
Sum of arcs in a circle is 360.
Substitution
Simplify.
Simplify.
Answer:
Find Arc Measures in Circle
Graphs
Sum of arcs in a circle is 360.
Substitution
Simplify.
Simplify.
Answer:
A. 124.3
B. 140.4
C. 155.6
D. 165.9
A. 124.3
B. 140.4
C. 155.6
D. 165.9
A. 273.6
B. 240.5
C. 215.7
D. 201.4
A. 273.6
B. 240.5
C. 215.7
D. 201.4
Use Arc Addition to Find Measures of Arcs
.
Use Arc Addition to Find Measures of Arcs
Arc Addition Postulate
= 58 + 32
= 90
Answer:
Substitution
Use Arc Addition to Find Measures of Arcs
Arc Addition Postulate
= 58 + 32
= 90
Answer:
Substitution
Use Arc Addition to Find Measures of Arcs
Use Arc Addition to Find Measures of Arcs
Arc Addition Postulate
= mIMJ + mJMK
= 90 + 58
= 148
Answer:
Substitution
Use Arc Addition to Find Measures of Arcs
Arc Addition Postulate
= mIMJ + mJMK
= 90 + 58
= 148
Answer:
Substitution
A. 180
B. 90
C. 52
D. 38
A. 180
B. 90
C. 52
D. 38
A. 52
B. 90
C. 142
D. 180
A. 52
B. 90
C. 142
D. 180
Find Arc Length
Arc Length Equation
Substitution
cm
Answer:
Use a calculator.
Find Arc Length
Arc Length Equation
Substitution
cm
Answer:
Use a calculator.
Find Arc Length
Arc Length Equation
Substitution
Use a calculator.
Answer:
Find Arc Length
Arc Length Equation
Substitution
Use a calculator.
Answer:
Find Arc Length
Arc Length Equation
Substitution
Use a calculator.
Answer:
Find Arc Length
Arc Length Equation
Substitution
Use a calculator.
Answer:
A. 3.56 cm
B. 3.77 cm
C. 3.98 cm
D. 4.21 cm
A. 3.56 cm
B. 3.77 cm
C. 3.98 cm
D. 4.21 cm
A. 36.56 cm
B. 37.79 cm
C. 38.61 cm
D. 40.21 cm
A. 36.56 cm
B. 37.79 cm
C. 38.61 cm
D. 40.21 cm
A. 32.99 cm
B. 33.59 cm
C. 33.89 cm
D. 34.61 cm
A. 32.99 cm
B. 33.59 cm
C. 33.89 cm
D. 34.61 cm