• Home

  • Documents

  • P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less...
24

P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Tags:

Embed Size (px)

Citation preview

Page 1: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters
Page 2: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

P

A

BC

Central Angle : An Angle whose vertex is at the center of the

circleMinor ArcMajor Arc

Less than 180°

More than 180°

ABACB

To name: use 2 letters

To name: use 3 letters

<APB is a Central Angle

Page 3: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

P

E

F

D

Semicircle: An Arc that equals 180°

EDF

To name: use 3 letters

EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of

180°

Page 4: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

THINGS TO KNOW AND REMEMBER ALWAYS

A circle has 360 degrees

A semicircle has 180 degrees

Vertical Angles are Equal

Linear Pairs are Supplementary

Page 5: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Vertical Angles are Equal

Page 6: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Linear Pairs are Supplementary

http://www.mathopenref.com/linearpair.html

120° 60°

Page 7: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

measure of an arc = measure of central angle

A

B

C

Q 96

m AB

m ACB

m AE

E

=

=

=

96°

264°

84°

Page 8: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Arc Addition PostulateA

B

C

m ABC =

m AB + m BC

Page 9: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Tell me the measure of the following arcs.

80100

40

140A

B

C

D

R

m DAB =

m BCA =

240

260

Page 10: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles.

4545

A

BC

D

110

Page 11: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Classwork

•Page 193 #9-18 You have 15 minutes.

Page 12: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Inscribed Angle: An angle whose

vertex is on the circle and

whose sides are chords of the circle

INSCRIBEDANGLE

INTER

CEP

TED

ARC

Page 13: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.

C

L

O

T1.

YES; CL

Page 14: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.

Q

R

K

V2. NO;

QVR

S

Page 15: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

2

ArcdIntercepteAngleInscribed

160°

80°

To find the measure of an inscribed angle…

Page 16: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

http://www.geogebra.org/

en/upload/files/english/Guy/

Circles_and_angles/Inscribed_Anlge.html

Page 17: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

120

x

What do we call this type of angle?What is the value of x?

y

What do we call this type of angle?How do we solve for y?The measure of the inscribed angle is HALF the

measure of the inscribed arc!!

Page 18: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_angle_practice.html

Page 19: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Examples

3. If m JK = 80, find m <JMK.

M

Q

K

S

J

4. If m <MKS = 56, find m MS.

40

112

Page 20: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

72

If two inscribed angles intercept the same arc, then they are congruent.

Page 21: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_angle_practice.html

Page 22: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Example 5

In J, m<A= 5x and m<B = 2x + 9.Find the value of x.

A

Q

D

JT

U

B

m<A = m<B 5x = 2x+9x = 3

Page 23: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Classwork:

•Page 193 #9-23•Page 207 #1-15

Page 24: P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters

Whatever is left is homework


All Triangles= 180 degrees. Right Triangle One angle is 90 (a right angle) Right Triangle One angle is 90 (a right angle) Scalene No sides or angles

All Triangles= 180 degrees. Right Triangle One angle is 90 (a right angle) Right Triangle One angle is 90 (a right angle) Scalene No sides or angles

Documents
Table of Contents · A. Which angle measures 90 degrees? B. Which angle is greater than 90 degrees but less than 180 degrees? C. Which angle is less than 90 degrees? D. Which angle

Table of Contents · A. Which angle measures 90 degrees? B. Which angle is greater than 90 degrees but less than 180 degrees? C. Which angle is less than 90 degrees? D. Which angle

Documents
An angle whose measure is less than 90° Acute Angle

An angle whose measure is less than 90° Acute Angle

Documents
Types of angles Definitions - Oasis Academy South Bank€¦ · Types of angles 1 Acute Less than 90° 2 Obtuse more than 90°, less than 180° 3 Reflex more than 180° 4 Straight

Types of angles Definitions - Oasis Academy South Bank€¦ · Types of angles 1 Acute Less than 90° 2 Obtuse more than 90°, less than 180° 3 Reflex more than 180° 4 Straight

Documents
Identify angles...2020/06/16  · 1 Complete the sentences. Use the word bank to help you. 90 180 greater less a) A right angle is degrees. b) An acute angle is than degrees. c) An

Identify angles...2020/06/16  · 1 Complete the sentences. Use the word bank to help you. 90 180 greater less a) A right angle is degrees. b) An acute angle is than degrees. c) An

Documents
Angle Theorems & Definitions (Review). Supplementary = 180 ° Complementary = 90°

Angle Theorems & Definitions (Review). Supplementary = 180 ° Complementary = 90°

Documents
Quadrilaterals and Circles - MacHighwayfrink.machighway.com/~dynamicm/gc-geometry-chap08.pdfthe Interior Angle Sum Theorem. S 180(n 2) Interior Angle Sum Theorem 180(6 2) n 6 180(4)

Quadrilaterals and Circles - MacHighwayfrink.machighway.com/~dynamicm/gc-geometry-chap08.pdfthe Interior Angle Sum Theorem. S 180(n 2) Interior Angle Sum Theorem 180(6 2) n 6 180(4)

Documents
2018 MATHEMATICS - iresource.gov.sb€¦ · Angle A 2 Angle B Angle C D. Angle A Angle B Angle C 180 . 7 15. The angle of elevation θ in the diagram below is; A. 22.62⁰ B. 24.62⁰

2018 MATHEMATICS - iresource.gov.sb€¦ · Angle A 2 Angle B Angle C D. Angle A Angle B Angle C 180 . 7 15. The angle of elevation θ in the diagram below is; A. 22.62⁰ B. 24.62⁰

Documents
Angle Measures - Clover Sitesstorage.cloversites.com/stalbertthegreatcatholicchurch/documents... · angle measures 180°. 3 12 11 10 9 8 ... PBJ, banana; water, PBJ, orange water

Angle Measures - Clover Sitesstorage.cloversites.com/stalbertthegreatcatholicchurch/documents... · angle measures 180°. 3 12 11 10 9 8 ... PBJ, banana; water, PBJ, orange water

Documents
Evolution 180 Camera Range - oncamgrandeye.com · 180 camera has an exceptionally wide viewing angle (187°). Consider the camera location for providing comprehensive coverage of

Evolution 180 Camera Range - oncamgrandeye.com · 180 camera has an exceptionally wide viewing angle (187°). Consider the camera location for providing comprehensive coverage of

Documents
MEASUREMENT AND GEOMETRY TOPIC 5 Geometry PROOFS - … · An acute angle is greater than 0°, but less than 90°. A right angle is an angle that equals exactly 90°. An obtuse angle

MEASUREMENT AND GEOMETRY TOPIC 5 Geometry PROOFS - … · An acute angle is greater than 0°, but less than 90°. A right angle is an angle that equals exactly 90°. An obtuse angle

Documents
Grosse Pointe Public School System / GPPS Home...Angle that measures exactly 900 Angle that measures less than 900 Angle that is more than 900 but less than 1800 Angle that measures

Grosse Pointe Public School System / GPPS Home...Angle that measures exactly 900 Angle that measures less than 900 Angle that is more than 900 but less than 1800 Angle that measures

Documents
Angles Type of angle: Acute: An Angle less than 90 degrees Right angle: An angle that is 90 degrees Obtuse angle: An angle more than 90 degrees Straight

Angles Type of angle: Acute: An Angle less than 90 degrees Right angle: An angle that is 90 degrees Obtuse angle: An angle more than 90 degrees Straight

Documents
Math Word List 5. Obtuse Angle An obtuse angle is more than 90° but less than 180° In other words, it is between a right angle and a straight angle

Math Word List 5. Obtuse Angle An obtuse angle is more than 90° but less than 180° In other words, it is between a right angle and a straight angle

Documents
1.2 Measurement of Segments and Angles. An acute angle is an angle whose measure is greater than 0 and less than 90 degrees. A right angle is an angle

1.2 Measurement of Segments and Angles. An acute angle is an angle whose measure is greater than 0 and less than 90 degrees. A right angle is an angle

Documents
NC300A Milling Machine Controller G Command Guidelines ......2013/02/01  · an arc of central angle ≤ 180 and an arc of central angle > 180 for the negative R value. In the figure

NC300A Milling Machine Controller G Command Guidelines ......2013/02/01  · an arc of central angle ≤ 180 and an arc of central angle > 180 for the negative R value. In the figure

Documents
Mark Scheme (Results) - qualifications.pearson.com · 14 Scheme 1 (interior angle and angle ADC and an angle in triangle ADC) Let X be midpoint of DC (Angle DEA =) 5 (5-2) × 180

Mark Scheme (Results) - qualifications.pearson.com · 14 Scheme 1 (interior angle and angle ADC and an angle in triangle ADC) Let X be midpoint of DC (Angle DEA =) 5 (5-2) × 180

Documents
Angle Geometry - WordPress.com · Angle Geometry Angle Properties Acute Angle is an angle that is more than 0° and less than 90°. Obtuse Angle is an angle greater than 90° and

Angle Geometry - WordPress.com · Angle Geometry Angle Properties Acute Angle is an angle that is more than 0° and less than 90°. Obtuse Angle is an angle greater than 90° and

Documents
2.1 Lines and Angles Acute angle – 0 < x < 90 Right angle - 90 Obtuse angle – 90 < x < 180 Straight angle - 180

2.1 Lines and Angles Acute angle – 0 < x < 90 Right angle - 90 Obtuse angle – 90 < x < 180 Straight angle - 180

Documents
1.2 Angle Measures & Angle Bisectors 4th hr.notebook...1.2 Angle Measures & Angle Bisectors 4th hr.notebook 6 September 07, 2016 28° 28° 119° 53 0 180 10 170 20 160 30 150 40 140

1.2 Angle Measures & Angle Bisectors 4th hr.notebook...1.2 Angle Measures & Angle Bisectors 4th hr.notebook 6 September 07, 2016 28° 28° 119° 53 0 180 10 170 20 160 30 150 40 140

Documents
The largest product range in mirrors - ProVia AB · 5 Symbol explanation Viewing angle 360, this mirror is a half sphere, allowing for any viewing angle. Viewing angle 180, this mirror

The largest product range in mirrors - ProVia AB · 5 Symbol explanation Viewing angle 360, this mirror is a half sphere, allowing for any viewing angle. Viewing angle 180, this mirror

Documents
Part 4 Equal and Greater Than 180 KW_published

Part 4 Equal and Greater Than 180 KW_published

Documents
Compare and order angles · 3 Circle the greatest angle in each diagram. 4 Here is an angle. a) Draw a smaller angle than 105° in the box on the left. b) Draw a greater angle than

Compare and order angles · 3 Circle the greatest angle in each diagram. 4 Here is an angle. a) Draw a smaller angle than 105° in the box on the left. b) Draw a greater angle than

Documents
angles their An angle€¦ · Acute angle—An angle with a measure between 0° and 90°. Obtuse angle—An angle with a measure between 90° and 180°. Straight angle—An angle

angles their An angle€¦ · Acute angle—An angle with a measure between 0° and 90°. Obtuse angle—An angle with a measure between 90° and 180°. Straight angle—An angle

Documents
2.4 - Angles Properties in a Quadrilateral Name:...2.4 - Angle Properties in Polygons A convex polygon is any polygon in which each interior angle measure less than 180°. A concave

2.4 - Angles Properties in a Quadrilateral Name:...2.4 - Angle Properties in Polygons A convex polygon is any polygon in which each interior angle measure less than 180°. A concave

Documents
Pre-Algebra Enrichment. Classifying Angles Acute angle- An angle that measures less than 90 degrees. Obtuse angle- An angle that measures more than 90

Pre-Algebra Enrichment. Classifying Angles Acute angle- An angle that measures less than 90 degrees. Obtuse angle- An angle that measures more than 90

Documents
MATH VOCABULARY Intermediate. Acute Angle An angle that measures less than a right angle (90°).angleright angle

MATH VOCABULARY Intermediate. Acute Angle An angle that measures less than a right angle (90°).angleright angle

Documents
180° Point Angle Solid Carbide Drills€¦ · 180° Point Angle Solid Carbide Drills. 180 ... The flat multidrill MDF type is a solid carbide drill that can be used for various purposes

180° Point Angle Solid Carbide Drills€¦ · 180° Point Angle Solid Carbide Drills. 180 ... The flat multidrill MDF type is a solid carbide drill that can be used for various purposes

Documents
Greater Than the Critical Angle

Greater Than the Critical Angle

Documents
28M 860SJ - Access Solutions · Working Height 28.21m Platform Rotation Angle 180 Jib Raise Angle 70 Jib Lower Angle 60 Jib Articulation Range 130 Maximum Horizontal Outreach 22.86m

28M 860SJ - Access Solutions · Working Height 28.21m Platform Rotation Angle 180 Jib Raise Angle 70 Jib Lower Angle 60 Jib Articulation Range 130 Maximum Horizontal Outreach 22.86m

Documents