1.
Section 1-4
Angle Measure
Monday, September 15, 14
2.
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
4.
Vocabulary
1. R a y : 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
5.
Vocabulary
1. R a y : 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
6.
Vocabulary
1. R a y : 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. An g l e : 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
7.
Vocabulary
1. R a y : 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. An g l e : 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
8.
Vocabulary
1. R a y : 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. An g l e : 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
9.
Vocabulary
1. R a y : 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. An g l e : 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. I n t e r i o r : 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
11.
Vocabulary
7. E x t e r i o r : 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
12.
Vocabulary
7. E x t e r i o r : 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
13.
Vocabulary
7. E x t e r i o r : 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
14.
Vocabulary
7. E x t e r i o r : 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
15.
Vocabulary
7. E x t e r i o r : 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
16.
Vocabulary
7. E x t e r i o r : 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
1 2 . A n g l e B i s e c t o r : A ray and splits an angle into two parts with equal
measure
Monday, September 15, 14
17.
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
18.
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
19.
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
20.
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
21.
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
22.
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
Monday, September 15, 14
23.
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
Monday, September 15, 14
24.
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
25.
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
26.
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
27.
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
28.
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
29.
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
30.
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
31.
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
32.
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
33.
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
34.
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
35.
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.
9x − 7
H G J
Monday, September 15, 14
36.
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.
9x − 7
7x + 13
H G J
Monday, September 15, 14
37.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
Monday, September 15, 14
38.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x − 7x
Monday, September 15, 14
39.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
Monday, September 15, 14
40.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
Monday, September 15, 14
41.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
Monday, September 15, 14
42.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
Monday, September 15, 14
43.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
x = 10
Monday, September 15, 14
44.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7
Monday, September 15, 14
45.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7 = 90 − 7
Monday, September 15, 14
46.
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.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7 = 90 − 7 = 83°
Monday, September 15, 14
48.
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
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