# WARM UP. Sunday, November 16, 2014

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1 WARM UP Sunday, November 16,

2 Objectives Use properties of circles to derive the formula for sector area. Determine arc length and arc measure for given central and inscribed angle measures Determine angle measures using the properties of interior angles. Homework Circle Packet, Sections I, II and III all problems

3 ALL Make Up Tests for the Log and Exponents Unit must be completed by Monday November 17 th. No exceptions. ALL Retakes for the Log and Exponents Unit must be completed by Friday November 21 st. No exceptions. You MUST bring your test corrections with you to be eligible for a retake. UNIT TEST THIS FRIDAY

4 Homework review: Sections III, IV and V

5 Homework review

6 Homework review

7 Homework review

8 Homework review

9 Homework review

10 Homework review

11 Homework review

12 Homework review

13 Homework review

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16 Homework review: Sections VI

17 Homework review: Mid-segment Theorem

18 Homework review: Triangles Section 6

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24 Circles: Just what are they good for? Apparently these people found a good use for them! We will find even better uses for circles.

25 Circumference C = 2πr Area A = πr 2 Diameter Radius The GUTS of a circle Divides the circle into two equal parts. Straight line connecting the center to the edge of the circle. Half the length of the diameter.

26 The GUTS of a circle Radius Every radius in the same circle is equal to all the other radii in the same circle. So what is the value of x? 5X-32 X 5x 32 = x x = 8

27 The GUTS of a circle A Chord Line drawn inside the circle that touches the circle at its endpoints. B Chords are named by their end points. C D

28 Circles guts C Central Angle Vertex is the center of the circle and it extends to the edge of the circle. A B ABC is a central angle

29 Circles guts F Inscribed Angle Vertex is on the edge of the circle and extends inward to the opposite edge of the circle. D DEF is an inscribed angle E

30 Quick Check What is the circumference of a circle? Did you say pi are squared? WRONG Pie are round!

31 Circles guts C Arc r = 5 Part of the circumference cut off by an angle. A 45 B An Arc can be referred to by its measure or its length. The measure of an Arcs is based on the central angle that intercepts the Arc. m ac = 45

32 Circles guts Arc C r = 5 The length of an Arc is based on its portion of the circumference. A 45 B What percentage of this circle s circumference does this arc represent? percent = part whole = = 1 8 The arc length is equal to this percentage time the circumference of the circle. l = 1 8 2πr = 1 8 2π(5) = 5 4 π

33 Circles guts Sectors A sector is like a pizza slice. It is a portion of the area of a circle. 90 r = 5 What percentage of this circle s area does this sector represent? percent = part whole = = 1 4 The sector area is equal to this percentage time the area of the circle. s = 1 4 πr2 = 1 4 π(52 ) = 25 4 π

34 Central Angles vs. Inscribed Angles A central angle is equal to the measure of its intercepted arc. m AOB = m AB = 80 An inscribed angle is equal to one half the measure of its intercepted arc. m ABC = 1 2 m AC = 50

35 Find X (no pointing) x = 113 x = 62 x = 192

36 Use the properties we just discussed to find the measure of angle ABC. What do you notice about angle ABC and angle ADC? They intercept the same arc! How does that help you determine the value of x? Because they intercept the same arc the two angles have the same measure. Therefore the measure of angle ABC is also 81 o.

37 More Inside Angles. But first a word about tangents.

38 There is a special relationship between tangents and the arcs they intercept. Notice these angles are inside the circle!

39 Write this formula down. It s not in your packet. (It s in your study guide) Tangent Chord Angle = 1 2 Intercepted arc MLK = 1 2 m KL = 1 2 (130) = 65

40 You try these two Find the measure of SRQ 73 Find the measure of major arc GF 208

41 Lets talk about angles formed by two intersecting chords. We can use the intercepted arcs to find angle measures. Angle formed inside by intersecting chords = 1 2 Sum of intersected arcs BED = 1 2 (m AC + m BD) = 1 ( ) 2 = 120

42 Sometimes we have to work backward Find m BC BDC = 1 2 (m BC + m AE) Use the formula 85 = 1 2 (m BC + 70) 170 = m BC = m BC Fill in what you know Solve for what you don t know

43 You try this one Find m UT UST = 1 2 (m UT + m VA) Use the formula 120 = 1 2 (m UT + 60) 240 = m UT = m UT Fill in what you know Solve for what you don t know

44 To Summarize Central Angle Inscribed Angle Intersecting Chord Angles Tangent Angle

45 PERFECT PRACTICE MAKES PERFECT! Work on your Circles packet. Problems in your study guide If you finish it today s assignment before you leave, you can accumulate credits for a 2 point addition to your unit test grade. You ll need 5 credits for 2 points.

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