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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