Angle Measure
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Transcript of Angle Measure
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Angle Measure
Sec: 1.4Sol: G.4d,e
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Ray
• Is Part of a line• Has one endpoint and extends indefinitely in
one direction.• Named by stating the endpoint and any other
point on the ray. (endpoint must be stated first.)
Denoted with an arrow pointing in one direction. AB
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Example
Named:Or
Note: E has to go first!!!
EF
G
EF EG
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Opposite Rays
• Two rays that fall on the same line, but go in opposite directions.
are opposite rays. They are also collinear rays.
Q P R
PRPQ,
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Angles
• Are formed By two non-collinear rays.• They have a common endpoint.• The two rays are called sides of an angle.• The common endpoint is the vertex.
A
C
BVertex
Side
Side AB
AC
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Lesson 1-4: Angles 7
There are three ways to name an angle
ABC or CBA
Using 3 points: The vertex must be the middle letter
This angle can be named as
Using 1 point: using only vertex letter (only used when there is only one angle present).
Since B is the vertex of only this angle, this can also be called .A
BC
B
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Lesson 1-4: Angles 8
Naming an Angle - continued
Using a number: when naming with a number you use the number on the interior of the angle.
2
* The “1 letter” name is unacceptable when …more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present.
2
A
B C
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Angles Continued
• Name the following angle.
A
C
B
4,,, CABBACA
4
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Lesson 1-4: Angles 10
Example
K
32
K
L
M
P
Therefore, there is NO in this diagram.There is , ,LKM PKM and LKP
2 3 5!!!There is also and but there is no
K is the vertex of more than one angle.
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Lesson 1-4: Angles 11
Angle and Points
Angles can have points in the interior, in the exterior or on the angle.
Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex.
A
BC
D
E
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Example
1.Name all angles with B as a vertex.
2. Name the sides of <5.
3. Write another name for <6.
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Classifying Angles:Right Angle Acute Angle Obtuse Angle Straight Angle
An angle whose measure is exactly 90°.
An angle whose measure is less than 90°
An angle whose measure is between 90° and 180°
An angle whose measure is exactly 180°
A B C
D
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Example
Classify each angle as right, obtuse, acute or straight.1. <TYV2. < WYT3. <TYU4. <TYX
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Congruent angles
• Two angles with the same angle measure(Note: Arcs on the angle signify that they are
congruent.)Example:
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Lesson 1-4: Angles 16
Angle Addition Postulate
R
M K
W
The sum of the two smaller angles will always equal the measure of the larger angle.
Complete:
m ____ + m ____ = m _____MRK KRW MRW
Postulate:
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Lesson 1-4: Angles 17
Adding Angles
22°
36°
21
D
B
C
A
Therefore, mADC = 58.
m1 + m2 = mADC also.
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Lesson 1-4: Angles 18
Example: Angle Addition
R
M K
W
3x + x + 6 = 90 4x + 6 = 90 – 6 = –64x = 84x = 21
K is interior to MRW, m MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK.
3xx+6 Are we done?
mMRK = 3x = 3•21 = 63º
First, draw it!
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Lesson 1-4: Angles 19
Example: Angle Addition
R
M K
W
K is interior to MRW, m MRK = (2x + 10), m KRW = (4x - 3) and mMRW = 145º. Find mMRK and m KRW.
2x + 10
4x - 3 How can you check this?
First, draw it!
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Angle Bisectors
• Is a ray that divides an angle into two congruent halves.
• bisects RPS,m RPQ = 3x+6°and the m∠QPS =4x-8° .Find m RPS.m RPS = m RPQ + m QPS
PQ
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Assignments
Classwork: Handout
Homework: Handout