1. 1. Find the x-intercept of the graph of y = x2 – 11x + 18. a. -3,-5
Warm Up
Friday, November 16, 2018
1. Find the x-intercept of the graph of y = x2 – 11x + 18.
a. -3,-5
b. 2,9
c. -2,-9
d. 3,5

2. Warm Up
2. Factor: 3x2 – x – 14
(x + 7)(3x – 2) c. (x – 7)( 3x + 2)
(3x – 7)(x + 2) d. (3x + 7)( x – 2)
3. Factor: 9y2 – 16
(3y + 4)(3y + 4) c. (3y + 4)( 3y – 4 )
(9y + 1)(y – 16) d. (3y – 4 )(3y – 4)
4. Find the value of x and y. x y 20
60o
5. In a 45o45o90o triangle, the ratio of the length of the hypotenuse to the length of a side is _____.

3. Essential Question: How do we name arcs and find the measure of arcs?
Find Arc Measures
Friday, November 16, 2018
Essential Question:
How do we name arcs and find the measure of arcs?
Lesson 6.2

4. Daily Homework Quiz
Is AB tangent to C?
Explain. . 1. 2.
Find x.
ANSWER
Yes; = 1156 = 34 so AB AC, and a line to a radius at its endpoint is tangent to the circle. 2
ANSWER 12

5. Arcs in a stained glass window

6. Gateway Arch, St. Louis, Missouri
Commemorates the Louisiana Purchase

7. World Largest Arched Bridge
Completed in 2009, span 1811 feet, length of the bridge
5712 feet. Located in Chongqing ,China.

8. New River Gorge Bridge in the largest arched bridge in the U. S
New River Gorge Bridge in the largest arched bridge in the U.S. Located in West Virginia (1,699 ft)

9. ARCS
Arcs :
The part or portion on the circle from some point B to C is called an arc. A B C
Example: B
Semicircle:
An arc that is equal to 180°. O A
Example: C

10. Minor Arc & Major Arc Minor Arc :
A minor arc is an arc that is less than 180°
A minor arc is named using its endpoints with an “arc” above. A
Example:
Major Arc:
A major arc is an arc that is greater than 180°. B B O
A major arc is named using its endpoints along with another point on the arc (in order). A
Example: C

11. Lesson 8-1: Circle Terminology
Example: ARCS
Identify a minor arc, a major arc, and a semicircle, given that is a diameter. A C D E F
Minor Arc:
Major Arc:
Semicircle:
Lesson 8-1: Circle Terminology

12. Central Angles is a central angle
A central angle is an angle whose vertex is the center of the circle and whose sides intersect the circle. A P B
is a central angle
Central Angle
(of a circle)
NOT A Central Angle
(of a circle)
Central Angle
(of a circle)

13. Measuring Arcs
The measure of an arc is the same as the measure of its associated central angle. A P B

14. GUIDED PRACTICE
Identifying arcs
Identify the given arc as a major arc, minor arc, or
semicircle, and find the measure of the arc. 1
. TQ
SOLUTION
TQ is a minor arc, so m TQ = 120o.
. QRT 2
SOLUTION
QRT is a major arc, so m QRT= 240o.

15. GUIDED PRACTICE
Identifying arcs
Identify the given arc as a major arc, minor arc, or
semicircle, and find the measure of the arc.
. TQR 3
SOLUTION
TQR is a semicircle, so m TQR = 180o.
. QS 4
SOLUTION
QS is a minor arc, so m QS = 160o.

16. Identifying arcs
Identify the given arc as a major arc, minor arc, or
semicircle, and find the measure of the arc.
. TS 5
SOLUTION
TS is a minor arc, so m TS = 80o.
. RST 6
SOLUTION
RST is a semicircle, so m RST = 180o.

17. Find measures of arcs
Find the measure of each arc of P, where RT is a diameter. RS 7.
RTS 8.
RST 9.
SOLUTION
RS is a minor arc, so mRS = m RPS = 110o. 7.
RTS is a major arc, so mRTS = 360o o = 250o. 8. – 9.
RT is a diameter, so RST is a semicircle, and mRST = 180o.

18. Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

19. Find measures of arcs
A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.
Survey
10.
mAC
SOLUTION
10.
mAC
mAB = +
mBC
= 29o + 108o
= 137o

20. Find measures of arcs
A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.
Survey
11.
mACD
SOLUTION
11.
mACD = mAC + mCD
= 137o + 83o
= 220o

21. EXAMPLE 2
Find measures of arcs
A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.
Survey
12.
mADC
SOLUTION
mADC
mAC
= 360o –
12.
= 360o – 137o
= 223o

22. EXAMPLE 2
Find measures of arcs
A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures.
Survey
13.
mEBD
SOLUTION
13.
mEBD = 360o – mED
= 360o – 61o
= 299o

23. Assignment
Page 193 #
Page 195 # 1 – 12.