10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center...

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10.2– Find Arc Measures

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Transcript of 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center...

Page 1: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

10.2– Find Arc Measures

Page 2: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Term Definition Picture

Central Angle

An angle whose vertex is the center of the circle

P

A

C

APC

Page 3: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Term Definition Picture

Minor Arc

Arc of a circle that is less than 180°

P

A

C

ACªTwo letters:

Page 4: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Term Definition Picture

Major Arc

Arc of a circle that is more than 180°

P

A

C

ABCº3 letters:

B

Page 5: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Term Definition Picture

Semicircle

Arc of a circle that is 180°

P

A

C

ABCº3 letters:

B

Page 6: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Term Definition Picture

Congruent circles

Two circles with the same radius

Page 7: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Term Definition Picture

Congruent arcs

Arcs that have the same central angle

A B

CD

ABª CDª

Page 8: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

The measure of a minor arc is the measure of its _____________ angle.central

P

A

Cx°

x°

Page 9: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

MNº

73°

73°

73°

minor

Page 10: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

NQª

73°107°

26°minor

Page 11: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

MPº

73°154°

26°minor

Page 12: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

MRPº

73°206°

26°

107°

major

Page 13: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

PNª

73°81°

26°

107°

minor

Page 14: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

MNQº

73°180°

26°

107°

semicircle

Page 15: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

MRQº

73°180°

26°

107°

Semicircle

Page 16: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

MRNº

73°287°

26°

107°

major

Page 17: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

10.4 – Use Inscribed Angles and Polygons

Page 18: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

An angle whose vertex is on a circle and whose sides are chords of the circle

Inscribed angle:

Page 19: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

An arc that is inside an inscribed angle

Intercepted Arc:

Page 20: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

A polygon that has all of its vertices on a circle

Inscribed Polygon :

Page 21: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

The circle that contains the vertices of a polygon

Circumscribed Circle:

Page 22: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

The measures of an inscribed angle is ________ the measure of its ______________ arc.

halfintercepted

D = AB 2

x°

2x°

Page 23: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

If two inscribed angles of a circle _____________ the same arc, then the angles are _____________.

interceptcongruent

D C

Page 24: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

A ________ triangle is inscribed in a circle iff the _______________ is a diameter of the circle.

righthypotenuse

B is a right angle because it inscribes a semicircle.

Page 25: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

A ____________________ can be inscribed in a circle iff its opposite angles are ______________.

quadrilateralsupplementary

mD + mF = 180°

mE + mG = 180°

Page 26: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the indicated measure.

=158 2

= 79°

Page 27: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the indicated measure.

=180 2

= 90°

180°

90°

Page 28: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the indicated measure.

= 40 2 = 80°

Page 29: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the indicated measure.

=

88°

92°

92 2

= 46°

Page 30: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the indicated measure.

=80 2

= 40°100°

80°

Page 31: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the indicated measure.

=56 2

= 28°

56°

Page 32: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the measure of A and C.

80°

mA =80 2

= 40°64°

mC =64 2

= 32°

Page 33: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the measure of A and C.

mA =146 2

= 73°

mC =62 2

= 31°

146°

62°

Page 34: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

mPNO = 68 2

= 34°

Page 35: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

mQNP = 62 2

= 31°

62°

Page 36: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

= 62°

62°

Page 37: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

= 130°

62°

Page 38: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

= 112°

62°

112°

Page 39: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

= 248°

62°

112°

Page 40: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Decide whether a circle can be circumscribed about the figure.

70 + 130 180

No,

Page 41: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Decide whether a circle can be circumscribed about the figure.

91 + 89 = 180

Yes,

91°

Page 42: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Decide whether a circle can be circumscribed about the figure.

115 + 63 180

No,

Page 43: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the value of the variables.

5x + 110 = 180

5x = 70

x = 14°

2y + 104 = 180

2y = 76

y = 38°

Page 44: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the value of the variables.

x + 108 = 180

x = 72°

y + y = 180

2y = 180

y = 90°

Page 45: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the value of the variables.

4x = 84+44 2

8x = 128

x = 16°

7y = 152+44 2

14y = 196

y = 14°

44°

1 1

Page 46: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

Find the value of the variables.

12x = 96+48 2

24x = 144

x = 6°

3y = 48+171 2

6y = 219

y = 36.5°

171°

1 1

Page 47: 10.2– Find Arc Measures. TermDefinitionPicture Central Angle An angle whose vertex is the center of the circle P A C.

10.210.4

662-663676-679

3-12, 16, 17, 22, 233-8, 11-15 odd, 16, 18

HW Problem

10.4 #15

3a = 54+66 2

6a = 120

a = 20°

4b = 66+110 2

8b = 176

b = 22°

66°1 1


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