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

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 _____.

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

Daily Homework Quiz Is AB tangent to C? Explain. . 1. 2. Find x. ANSWER Yes; 16 + 30 = 1156 = 34 so AB AC, and a line to a radius at its endpoint is tangent to the circle. 2 ANSWER 12

Arcs in a stained glass window http://free-stainedglasspatterns.com/2curvesround.html

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

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

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)

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

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

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

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)

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

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.

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.

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.

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 110o = 250o. 8. – 9. RT is a diameter, so RST is a semicircle, and mRST = 180o.

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

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

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

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

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

Assignment Page 193 # 1 -18. Page 195 # 1 – 12.