1. A rectangular plaza has a surrounding circular fence
A rectangular plaza has a surrounding circular fence. The diagonals of the rectangle pass from one point on the fence through the center of the circle to another point on the fence. Based on the information in the figure, what is the diameter of the fence? Round your answer to the nearest tenth of a foot.
Problem of the Day

2. Section 10-2a Measuring Angles and Arcs

3. Then
Now
Objectives
You measured angles and identified congruent angles.
Identify central angles, major arcs, minor arcs, and semicircles, and find their measures.

4. Common Core State Standards
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
4) Model with mathematics.
6) Attend to precision.
Common Core State Standards

5. A central angle of a circle is an angle with a vertex in the center of the circle. Its sides contain two radii of the circle. ∠ABC is a central angle of circle B.
Vocabulary

7. Find the value of x.
Example 1

8. Find the value of x.
Example 1

9. An arc is a portion of a circle defined by two endpoints.
Vocabulary

11. 𝐴𝐶 and 𝐷𝐵 are diameters of ⨀Q
𝐴𝐶 and 𝐷𝐵 are diameters of ⨀Q. Identify each arc as a major arc, minor arc, or semicircle of the circle. Then find its measure. 1. m 𝐴𝐸 2. m 𝐴𝐵 3. m 𝐸𝐷𝐶 4. m 𝐴𝐷𝐶 5. m 𝐴𝐵𝐶 6. m 𝐵𝐶
Examples 2 & 4

12. 𝐹𝐻 and 𝐸𝐺 are diameters of ⨀P. Find each measure. 1. m 𝐸𝐹 2. m 𝐷𝐸 3
𝐹𝐻 and 𝐸𝐺 are diameters of ⨀P. Find each measure. 1. m 𝐸𝐹 2. m 𝐷𝐸 3. m 𝐹𝐺 4. m 𝐷𝐻𝐺 5. m 𝐷𝐹𝐺 6. m 𝐷𝐺𝐸
Examples 2 & 4

13. 𝑃𝑅 and 𝑄𝑇 are diameters of ⨀A. Find each measure. 1. m 𝑈𝑃𝑄 2. m 𝑃𝑄𝑅 3
𝑃𝑅 and 𝑄𝑇 are diameters of ⨀A. Find each measure. 1. m 𝑈𝑃𝑄 2. m 𝑃𝑄𝑅 3. m 𝑈𝑇𝑆 4. m 𝑅𝑆 5. m 𝑅𝑆𝑈 6. m 𝑆𝑇𝑃 7. m 𝑃𝑄𝑆 8. m 𝑃𝑅𝑈
Examples 2 & 4

14. p.710 #12 – 15, 26 – 35, 67 – 69
Homework