Section 1-4Angle Measure

Monday, September 15, 14

Essential Questions

✤ How do you measure and classify angles?

✤ How do you identify and use congruent angles and the bisector of an angle?

Monday, September 15, 14

Vocabulary

1. Ray:

2. Opposite Rays:

3. Angle:

4. Side:

5. Vertex:

6. Interior:

Monday, September 15, 14

Vocabulary

1. Ray: Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB

2. Opposite Rays:

3. Angle:

4. Side:

5. Vertex:

6. Interior:

Monday, September 15, 14

Vocabulary

1. Ray: Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB

2. Opposite Rays: Rays that share an endpoint and are collinear

3. Angle:

4. Side:

5. Vertex:

6. Interior:

Monday, September 15, 14

Vocabulary

1. Ray: Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB

2. Opposite Rays: Rays that share an endpoint and are collinear

3. Angle: Two noncollinear rays that share an endpoint; uses three points or a listed number to name ∠ABC or ∠5

4. Side:

5. Vertex:

6. Interior:

Monday, September 15, 14

Vocabulary

1. Ray: Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB

2. Opposite Rays: Rays that share an endpoint and are collinear

3. Angle: Two noncollinear rays that share an endpoint; uses three points or a listed number to name ∠ABC or ∠5

4. Side: One of the rays that makes up an angle

5. Vertex:

6. Interior:

Monday, September 15, 14

Vocabulary

1. Ray: Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB

2. Opposite Rays: Rays that share an endpoint and are collinear

3. Angle: Two noncollinear rays that share an endpoint; uses three points or a listed number to name ∠ABC or ∠5

4. Side: One of the rays that makes up an angle

5. Vertex: The shared endpoint of the two rays that make up an angle

6. Interior:

Monday, September 15, 14

Vocabulary

1. Ray: Part of a line; has an endpoint and goes on forever in one direction; ray AB: AB

2. Opposite Rays: Rays that share an endpoint and are collinear

3. Angle: Two noncollinear rays that share an endpoint; uses three points or a listed number to name ∠ABC or ∠5

4. Side: One of the rays that makes up an angle

5. Vertex: The shared endpoint of the two rays that make up an angle

6. Interior: The part of an angle that is inside the two rays of the angle (the part that is less than 180° in measure)

Monday, September 15, 14

Vocabulary

7. Exterior:

8. Degree:

9. Right Angle:

10. Acute Angle:

11. Obtuse Angle:

12. Angle Bisector:

Monday, September 15, 14

Vocabulary

7. Exterior: The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure)

8. Degree:

9. Right Angle:

10. Acute Angle:

11. Obtuse Angle:

12. Angle Bisector:

Monday, September 15, 14

Vocabulary

7. Exterior: The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure)

8. Degree: The unit of measurement of an angle

9. Right Angle:

10. Acute Angle:

11. Obtuse Angle:

12. Angle Bisector:

Monday, September 15, 14

Vocabulary

7. Exterior: The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure)

8. Degree: The unit of measurement of an angle

9. Right Angle: An angle that is 90° in measure

10. Acute Angle:

11. Obtuse Angle:

12. Angle Bisector:

Monday, September 15, 14

Vocabulary

7. Exterior: The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure)

8. Degree: The unit of measurement of an angle

9. Right Angle: An angle that is 90° in measure

10. Acute Angle: An angle that is less than 90° in measure

11. Obtuse Angle:

12. Angle Bisector:

Monday, September 15, 14

Vocabulary

7. Exterior: The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure)

8. Degree: The unit of measurement of an angle

9. Right Angle: An angle that is 90° in measure

10. Acute Angle: An angle that is less than 90° in measure

11. Obtuse Angle: An angle that is more than 90° in measure

12. Angle Bisector:

Monday, September 15, 14

Vocabulary

7. Exterior: The part of an angle that is outside the two rays of the angle (the part that is greater than 180° in measure)

8. Degree: The unit of measurement of an angle

9. Right Angle: An angle that is 90° in measure

10. Acute Angle: An angle that is less than 90° in measure

11. Obtuse Angle: An angle that is more than 90° in measure

12. Angle Bisector: A ray and splits an angle into two parts with equal measure

Monday, September 15, 14

Example 1

Use the figure.

a. Name all angles that have C as a vertex.

b. Name the sides of ∠7.

c. Write another name for ∠4.

Monday, September 15, 14

Example 1

Use the figure.

a. Name all angles that have C as a vertex.

∠ACB,∠BCD,∠DCG,∠GCA

b. Name the sides of ∠7.

c. Write another name for ∠4.

Monday, September 15, 14

Example 1

Use the figure.

a. Name all angles that have C as a vertex.

∠ACB,∠BCD,∠DCG,∠GCA

b. Name the sides of ∠7.

DE, DF

c. Write another name for ∠4.

Monday, September 15, 14

Example 1

Use the figure.

a. Name all angles that have C as a vertex.

∠ACB,∠BCD,∠DCG,∠GCA

b. Name the sides of ∠7.

DE, DF

c. Write another name for ∠4.

∠IGD

Monday, September 15, 14

Example 2

Use the figure. Measure the angles listed and classify as either acute, right, or obtuse.

a. m∠AFC

b. m∠EFB

c. m∠EFD

Monday, September 15, 14

Example 2

Use the figure. Measure the angles listed and classify as either acute, right, or obtuse.

a. m∠AFC

b. m∠EFB

c. m∠EFD

http://www.chutedesign.co.uk/design/protractor/protractor.gifMonday, September 15, 14

Example 2

Use the figure. Measure the angles listed and classify as either acute, right, or obtuse.

a. m∠AFC

b. m∠EFB

c. m∠EFD

http://www.chutedesign.co.uk/design/protractor/protractor.gifMonday, September 15, 14

Example 2

Use the figure. Measure the angles listed and classify as either acute, right, or obtuse.

a. m∠AFC

b. m∠EFB

c. m∠EFD

http://www.chutedesign.co.uk/design/protractor/protractor.gif

90°, Right

Monday, September 15, 14

Example 2

Use the figure. Measure the angles listed and classify as either acute, right, or obtuse.

a. m∠AFC

b. m∠EFB

c. m∠EFD

http://www.chutedesign.co.uk/design/protractor/protractor.gif

90°, Right

Monday, September 15, 14

Example 2

Use the figure. Measure the angles listed and classify as either acute, right, or obtuse.

a. m∠AFC

b. m∠EFB

c. m∠EFD

http://www.chutedesign.co.uk/design/protractor/protractor.gif

90°, Right

Monday, September 15, 14

Example 2

Use the figure. Measure the angles listed and classify as either acute, right, or obtuse.

a. m∠AFC

b. m∠EFB

c. m∠EFD

http://www.chutedesign.co.uk/design/protractor/protractor.gif

90°, Right

165°, Obtuse

Monday, September 15, 14

Example 2

Use the figure. Measure the angles listed and classify as either acute, right, or obtuse.

a. m∠AFC

b. m∠EFB

c. m∠EFD

http://www.chutedesign.co.uk/design/protractor/protractor.gif

90°, Right

165°, Obtuse

51°, Acute

Monday, September 15, 14

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

Monday, September 15, 14

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

Monday, September 15, 14

B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x + 7 + 7

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x + 7 + 7

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x + 7 + 7

2x = 20

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x + 7 + 7

2x = 202 2

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x + 7 + 7

2x = 202 2

x = 10

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x + 7 + 7

2x = 202 2

x = 10

m∠HGR = 9(10) − 7

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x + 7 + 7

2x = 202 2

x = 10

m∠HGR = 9(10) − 7 = 90 − 7

Monday, September 15, 14

R B

Example 3

GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and m∠RGB = 7x + 13, find m∠HGR.

H G J

9x − 7

7x + 13

9x − 7 = 7x + 13− 7x− 7x + 7 + 7

2x = 202 2

x = 10

m∠HGR = 9(10) − 7 = 90 − 7 = 83°

Monday, September 15, 14

Problem Set

Monday, September 15, 14

Problem Set

p. 41 #1-41 odd, 51

“If we all did the things we are capable of doing, we would literally astound ourselves.” - Thomas A. Edison

Monday, September 15, 14