Arcs and Chords Chapter 10-2. Lesson 2 MI/Vocab central angle arc minor arc major arc semicircle Recognize major arcs, minor arcs, semicircles, and central.

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Presentation transcript:

Arcs and Chords Chapter 10-2

Lesson 2 MI/Vocab central angle arc minor arc major arc semicircle Recognize major arcs, minor arcs, semicircles, and central angles and their measures. Find arc length. Standard 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key)

Central Angle An angle whose vertex is the center of the circle Central Angle C B A  BCA is a Central Angle The sum of the central angles of a circle = 360 o –As long as they don’t overlap

Lesson 2 Ex1

A.A B.B C.C D.D Lesson 2 CYP1 A.9 B.21 C.65 D.30

A.A B.B C.C D.D Lesson 2 CYP1 A.15 B.25 C.40 D.75

Arcs Def:A portion of a circle cut by two radii Minor Arc—an arc formed by the interior of two radii with a central angle less than 180 o Major Arc—an arc formed by the exterior of two radii with a central angle less than 180 o Semi-Circle—an arc formed by the endpoints of a diameter The measure of an arc is equal to the measure of the central angle that forms it Two arcs are  if and only if their corresponding central angles are . (in the same circle or  circles) Animation: Arcs of a Circle

Minor Arc Major Arc m ADB = 300  60  P B A D m AB = 60 

Find the arc measures 80  45  180  125  55  305  m DFB = m AB = m DE = m AF = m DF = m BF = m BD = m FE = 135  45  55 

Arc Addition The measure of an arc formed by two adjacent arcs is the sum of the measures of the 2 arcs m DA = 72  mDC = 32  mCA = 40  B D A C m CA + m DC = 72 

Arc Addition Sample Problem Find m  ABD m  ABD = 48  m CA + m DC = m AD = m  ABD m AC = 4x + 7  m CD = 2x + 5  B D A C 8x  4x x + 5 = 8x 6x + 12 = 8x 12 = 2x 6 = x m  ABD = 8(6)

Lesson 2 Ex2 Measures of Arcs 46 o

Lesson 2 Ex2 Measures of Arcs is a minor arc, so is a semicircle. Answer: o

Lesson 2 Ex2 Measures of Arcs 46 o Answer: 67

Lesson 2 Ex2 Measures of Arcs 46 o 44 o Answer: 316

Lesson 2 CYP2 1.A 2.B 3.C 4.D A.54 B.27 C.108 D.72

Lesson 2 CYP2 1.A 2.B 3.C 4.D A.54 B.126 C.108 D.72

Lesson 2 CYP2 1.A 2.B 3.C 4.D A.126 B.234 C.180 D.288

Lesson 2 Ex3 A. BICYCLES This graph shows the percent of each type of bicycle sold in the United States in Find the measurement of the central angle representing each category. Circle Graphs

Lesson 2 Ex3 Circle Graphs B. BICYCLES This graph shows the percent of each type of bicycle sold in the United States in Is the arc for the wedge named Youth congruent to the arc for the combined wedges named Other and Comfort? Answer: no

Arc Length Arc Length Arc length is a part of the circumference of a circle. OR

Find the Arc Length of AB mAB = 60 o A B r = 12 cm

Lesson 2 Ex4 Arc Length In and. Write a proportion to compare each part to its whole.

Lesson 2 Ex4 Arc Length Now solve the proportion for. Simplify. degree measure of arc degree measure of whole circle arc length circumference Multiply each side by 9. Answer: The length of is π units or about 3.14 units.

A.A B.B C.C D.D Lesson 2 CYP4 A.7.88 B C D.24.74

Homework Chapter 10.2 Pg , all