1. UNIT: 1.1 - Tools of Geometry LESSON: 1.2a – Angles
4/27/2017
9/17/15
CC Geometry
UNIT: Tools of Geometry
LESSON: 1.2a – Angles
MAIN IDEA: Students will be able to use information to determine the measure of angles and explain relationships between angles.
HOMEWORK: Textbook
Page 41 #’s 9-10
Page 51 #’s 19-26
Take home quiz due Monday 9/21

2. Angle and Points ray vertex ray
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Angle and Points
An Angle is a figure formed by two rays with a common endpoint, called the vertex.
ray
vertex
ray
Angles can have points in the interior, in the exterior or on the angle. A E D B C
Points A, B and C are on the angle. D is in the interior and E is in the exterior.
B is the vertex.

3. 4/27/2017
Naming an angle: (1) Using 3 points (2) Using 1 point (3) Using a number – next slide
Using 3 points:
vertex must be the middle letter
This angle can be named as
Using 1 point:
using only vertex letter
* Use this method is permitted when the vertex point is the vertex of one and only one angle.
Since B is the vertex of only this angle, this can also be called A C B

4. Naming an Angle - continued
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Naming an Angle - continued
Using a number:
A number (without a degree symbol) may be used as the label or name of the angle. This number is placed in the interior of the angle near its vertex. The angle to the left can be named as A B 2 C
* 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.

5. Example Therefore, there is NO in this diagram.
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Example
K is the vertex of more than one angle.
Therefore, there is NO in this diagram.
There is

6. 4 Types of Angles Acute Angle: Right Angle: Obtuse Angle:
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4 Types of Angles
Acute Angle:
an angle whose measure is less than 90.
Right Angle:
an angle whose measure is exactly 90 .
Obtuse Angle:
an angle whose measure is between
90 and 180.
Straight Angle:
an angle that is exactly 180 .

7. 4/27/2017
Adding Angles
When you want to add angles, use the notation m1, meaning the measure of 1.
If you add m1 + m2, what is your result?
m1 + m2 = 58.
m1 + m2 = mADC also.
Therefore, mADC = 58.

8. Angle Addition Postulate
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Angle Addition Postulate
Postulate:
The sum of the two smaller angles will always equal the measure of the larger angle.
Complete:
m  ____ + m  ____ = m  _____
MRK
KRW
MRW

9. Example: Angle Addition
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Example: Angle Addition
K is interior to MRW, m  MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK.
First, draw it!
3x + x + 6 = 90
4x + 6 = 90
– 6 = –6
4x = 84
x = 21 3x
x+6
Are we done?
mMRK = 3x = 3•21 = 63º

10. 4/27/2017
Angle Bisector
An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles.
Example:
Since 4   6, is an angle bisector. 5 3

11. Congruent Angles Definition:
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Congruent Angles
Definition:
If two angles have the same measure, then they are congruent.
Congruent angles are marked with the same number of “arcs”.
The symbol for congruence is  3 5
Example:
3   5.

12. Example Draw your own diagram and answer this question:
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Example
Draw your own diagram and answer this question:
If is the angle bisector of PMY and mPML = 87, then find:
mPMY = _______
mLMY = _______

13. Complementary Angles Two angles are called complementary angles if the
sum of their degree measurements equals 90 degrees.
Example:
These two angles are complementary. Their sum is 90˚.
                                                      
58° + 32° = 90°

14. Complementary Angles
These two angles can be "pasted" together to form a right angle! Adjacent complementary angles.

15. Supplementary Angles
Two angles are called supplementary angles if the sum
of their degree measurements equals 180 degrees.
Example:
These two angles are supplementary. The sum of their measures is 180˚
                                                                      
139° +41° = 180 °

16. Linear Pair of Angles Special Supplementary Angles
Two angles that share a vertex and a side to form a line.
Two angles that can be "pasted" together to form a straight line!

17. Vertical Angles
Opposite angles formed by intersecting lines .     
For any two lines that meet, such as in the diagram below,
angle AEB and angle DEC are called vertical angles.
Angle BEC and angle AED are also vertical angles.
Vertical angles are congruent - have the same degree measurement.          
110 70 70
110

18. Review State whether the following are acute, right, or obtuse. 1. 3.5.
acute
obtuse
right 2. 4. ?
acute
obtuse ?

19. Complementary and Supplementary
Find the missing angle.
1. Two angles are complementary. One measures 65 degrees.
2. Two angles are supplementary. One measures 140 degrees.
Answer : 25
Answer : 40

20. Complementary and Supplementary
Find the missing angle. You do not have a protractor.
Use the clues in the pictures. 2. 1. x x 55
165
x = 180° – 165°
x = 90° – 55°
x = 15°
x = 35 °

21. Vertical Angles
Find the missing angle.
x = 58 x 58

22. More drawings F E 20 70 90 Box in the corner indicates a right angle.J 20 H

23. Final Drawing Find the measure of each missing angle B C 68 60 52 A G

24. Exit Ticket
Explain why angle 1 is congruent to angle 3.