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Chapter 1: Essentials of Geometry Name __________________________ Sections 4 & 5 Geometry Notes
Measuring & Classifying Angles
This should look familiar – name all of the geometric figures this represents:
Let’s use two rays and add another geometric figure to our knowledge banks: the
___________________. An angle is formed by two ____________________ rays with a
______________________ endpoint, or ___________________. The two rays are the
__________________of the angle. Label the angle figure below:
An angle can be named in several different ways. The angle above can be identified by its:
___________________, if it has one: ____________
___________________, if there is no other angle with vertex at O: ____________
___________________, remembering to keep the vertex letter in the middle: ____________
Try it! Name all of the points:
Name all of the rays:
Name 3 angles:
Name in another way:
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 2 of 12
Angle measures can be discussed in a ________________ way or measured more
____________________ using a ___________________. The measurement on the protractor is
described using _______________, which is the number and this symbol: _____.
Label the angle figure below:
Angles are classified in these general categories:
Looks like …
Is called …
Measures …
Use the diagram to estimate the measurement of:
1. ________
2. ________
3. ________
4. ________
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 3 of 12
Practice a few …
First, estimate the measure of each angle. Then, use your protractor to check your guess.
Use your protractor to draw angles with the given measures. Include points so that the names of the angles are correct.
° °
Now, add a ray that bisects each of your angles above… 1. How are you going to do that?
Find the ____________________
2. What do you think geometry calls that ray?
You got it! An angle _________________________
3. Label your new ray with point M.
4. What can you now say about each angle pair?
________ ________
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 4 of 12
Kinda obvious, right? So, you know what that means….Postulates!
#3: Protractor Postulate
• The rays __________ and __________ can be
matched with real numbers from _____ to _____.
• The _________________ of ___________ is equal to
the absolute value of the difference between
the numbers.
#4: Angle Addition Postulate
If P is in the _______________ of , then the
________ ________ ________.
Now, remember the difference between ?
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 5 of 12
Practice
Page 28 – 32 ALL: 3 – 5, 15 – 20; 22 – 24; 33 – 38; 57 – 61
C’mon! This is fun…you know there is more!
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 6 of 12
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 7 of 12
56. ______________________
57. ______________________
58 _______________________
59. ______________________
60. ______________________
61. ______________________
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 8 of 12
Angle Pairs
Let’s define a few more things about angles …
Angle Pair & Definition: Looks like:
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 9 of 12
Assumptions & Figures
List at least five things that you might assume about this
figure:
1.
2.
3.
4.
5.
An _______________________, much like a postulate, is something we believe to be true without
proof. Euclidean geometry is based on _____________________ that are careful assumptions.
However, we must be careful not to assume too much or we can get into trouble.
You MAY Assume: You MAY NOT Assume (unless marked):
Things that look _________________ are
straight
_______________ measurements and relative
____________ of figures
Points of ________________________ are
shown accurately
_________________________ (||) or
_________________________ (|) lines
Points shown on a line are
_____________________. _________________________ (≅ )
Unless planes are drawn, all points shown
are ______________________.
Relative positions of points are
____________________.
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 10 of 12
Because we cannot assume figures are parallel, perpendicular, or congruent, we use special markings on figures.
Marks like these:
Show:
Practice
Page 38 – 39: 6 – 11 ALL
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 11 of 12
Page 39: 12 – 15 ALL; 20 – 27 ALL
Page 39: Your choice of one 31, 32, or 33:
Chapter 1: Essentials of Geometry ................................................................................... Sections 4 & 5
Page 12 of 12
Page 40: 34 – 38 ALL:
Page 40: Your choice of one 39, 40, or 41:
Page 40: Your choice of one 42, 43, or 44:
