Five-Minute Check (over Chapter 8) Mathematical Practices Then/Now New Vocabulary Key Concept: Special Segments in a Circle Example 1: Identify Segments in a Circle Key Concept: Radius and Diameter Relationships Example 2: Find Radius and Diameter Key Concept: Circle Pairs Example 3: Find Measures in Intersecting Circles Key Concept: Circumference Example 4: Real-World Example: Find Circumference Example 5: Find Diameter and Radius Example 6: Standardized Test Example: Circumference of Circumscribed Polygons Lesson Menu

A. B. C. D. 5-Minute Check 1

A. B. C. D. 5-Minute Check 2

A. STW B. VWT C. WVU D. WRS 5-Minute Check 3

Find the length of the image of MN under a dilation with scale factor k = 3 and MN = 9. ___ A. 6 B. 18 C. 24 D. 27 5-Minute Check 4

Find the magnitude and direction of for A(4, 2) and B(–2, –1). 5-Minute Check 5

Which of the following transformations does not preserve length? A. dilation B. reflection C. rotation D. translation 5-Minute Check 6

Mathematical Practices 4 Model with mathematics. 1 Make sense of problems and persevere in solving them. Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.C.1 Prove that all circles are similar. G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. MP

You identified and used parts of parallelograms. Identify and use parts of a circle. Solve problems involving the circumference of a circle. Then/Now

circle concentric circles circumference pi () inscribed circumscribed center radius chord diameter Vocabulary

Concept

A. Name the circle and identify a radius. Identify Segments in a Circle A. Name the circle and identify a radius. Example 1

B. Identify a chord and a diameter of the circle. Identify Segments in a Circle B. Identify a chord and a diameter of the circle. Example 1

A. Name the circle and identify a radius. B. C. D. Example 1

B. Which segment is not a chord? Example 1

Concept

If RT = 21 cm, what is the length of QV? Find Radius and Diameter If RT = 21 cm, what is the length of QV? RT is a diameter and QV is a radius. d = 2r Diameter Formula 21 = 2r d = 21 10.5 = r Simplify. Answer: QV = 10.5 cm Example 2

If QS = 26 cm, what is the length of RV? A. 12 cm B. 13 cm C. 16 cm D. 26 cm Example 2

Concept

Find Measures in Intersecting Circles Example 3

Find Measures in Intersecting Circles Since the diameter of is 16 units, WY = 8. Similarly, the diameter of is 22 units, so XZ = 11. WZ is part of radius XZ and part of radius WY. First, find ZY. WZ + ZY = WY 5 + ZY = 8 ZY = 3 Next, find XY. XZ + ZY = XY 11 + 3 = XY 14 = XY Example 3

Find Measures in Intersecting Circles Answer: XY = 14 units Example 3

A. 3 in. B. 5 in. C. 7 in. D. 9 in. Example 3

Concept

C = d Circumference formula = (60) Substitution = 60 Simplify. Find Circumference CROP CIRCLES A series of crop circles was discovered in Alberta, Canada, on September 4, 1999. The largest of the three circles had a radius of 30 feet. Find its circumference. Since the radius is 30 feet, and d = 2r, the diameter = 2(30) or 60 feet. C = d Circumference formula = (60) Substitution = 60 Simplify. ≈ 188.50 Use a calculator. Answer: The circumference of the crop circle is 60 feet or about 188.50 feet. Example 4

The Unisphere is a giant steel globe that sits in Flushing Meadows-Corona Park in Queens, New York. It has a diameter of 120 feet. Find its circumference. A. 377.0 feet B. 392.5 feet C. 408.3 feet D. 422.1 feet Example 4

Circumference Formula Find Diameter and Radius Find the diameter and the radius of a circle to the nearest hundredth if the circumference of the circle is 65.4 feet. Circumference Formula Substitution Divide each side by . Use a calculator. Example 5

Radius Formula Use a calculator. Answer: d ≈ 20.82 ft; r ≈ 10.41 ft Find Diameter and Radius Radius Formula Use a calculator. Answer: d ≈ 20.82 ft; r ≈ 10.41 ft Example 5

Find the radius of a circle to the nearest hundredth if its circumference is 16.8 meters. A. 8.4 m B. 5.35 m C. 2.67 m D. 16.8 m Example 5

Circumference of Circumscribed Polygon Read the Test Item You need to find the diameter of the circle and use it to calculate the circumference. Example 6

Take the square root of each side. Circumference of Circumscribed Polygon Solve the Test Item The radius of the circle is the same length as either leg of the triangle. The legs of the triangle have equal length. Call the length x. Pythagorean Theorem Substitution Simplify. Divide each side by 2. Take the square root of each side. Example 6

So the radius of the circle is 3. Circumference of Circumscribed Polygon So the radius of the circle is 3. Circumference formula Substitution Answer: 6 units Example 6

A. B. C. D. Example 6