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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 Lesson Menu

Name a radius. A. B. C. D. 5-Minute Check 1

Name a chord. A. LF B. MF C. OM D. NF ___ 5-Minute Check 2

Name a diameter. A. OM B. OL C. NF D. MF ___ ____ 5-Minute Check 3

Refer to the figure. Find BC. A. 2 B. 3 C. 4 D. 5 5-Minute Check 4

Refer to the figure. Find DE. A. 9 B. 11 C. 13 D. 15 5-Minute Check 5

Find the length of the radius of the circle. A. 6.5 in. B. 10.9 in. C. 13 in. D. 17 in. 5-Minute Check 6

Mathematical Practices 6 Attend to precision. 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. CCSS

You measured angles and identified congruent angles. Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. Find arc lengths. Then/Now

central angle arc length arc minor arc major arc semicircle congruent arcs adjacent arcs Vocabulary

Concept

Find Measures of Central Angles Find the value of x. Example 1

The sum of the measures of 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 Example 1

Find the value of x. A. 9 B. 10 C. 11 D. 65 Example 1

Concept

Classify Arcs and Find Arc Measures Answer: Example 2

Classify Arcs and Find Arc Measures Example 2

Classify Arcs and Find Arc Measures Answer: Example 2

Classify Arcs and Find Arc Measures Answer: Example 2

A. B. C. D. Example 2

A. B. C. D. Example 2

A. B. C. D. Example 2

Concept

mLPK = 0.21(360) Find 21% of 360. = 75.6 Simplify. Answer: Find Arc Measures in Circle Graphs mLPK = 0.21(360) Find 21% of 360. = 75.6 Simplify. Answer: Example 3

Find Arc Measures in Circle Graphs Example 3

Sum of arcs in a circle is 360. Find Arc Measures in Circle Graphs Sum of arcs in a circle is 360. Substitution Simplify. Simplify. Answer: Example 3

A. 124.3 B. 140.4 C. 155.6 D. 165.9 Example 3

A. 273.6 B. 240.5 C. 215.7 D. 201.4 Example 3

Concept

Use Arc Addition to Find Measures of Arcs . Example 4

Arc Addition Postulate Use Arc Addition to Find Measures of Arcs Arc Addition Postulate = 58 + 32 Substitution = 90 Answer: Example 4

Use Arc Addition to Find Measures of Arcs Example 4

Arc Addition Postulate Use Arc Addition to Find Measures of Arcs Arc Addition Postulate = mIMJ + mJMK = 90 + 58 Substitution = 148 Answer: Example 4

A. 180 B. 90 C. 52 D. 38 Example 4

A. 52 B. 90 C. 142 D. 180 Example 4

Concept

Arc Length Equation Substitution cm Use a calculator. Answer: Find Arc Length Arc Length Equation Substitution Use a calculator. cm Answer: Example 5

Arc Length Equation Substitution Use a calculator. Answer: Find Arc Length Arc Length Equation Substitution Use a calculator. Answer: Example 5

Arc Length Equation Substitution Use a calculator. Answer: Find Arc Length Arc Length Equation Substitution Use a calculator. Answer: Example 5

A. 3.56 cm B. 3.77 cm C. 3.98 cm D. 4.21 cm Example 5

A. 36.56 cm B. 37.79 cm C. 38.61 cm D. 40.21 cm Example 5

A. 32.99 cm B. 33.59 cm C. 33.89 cm D. 34.61 cm Example 5

End of the Lesson