Download 1-4 Exploration Activity with Angles - Sulkes

Name: ______________________________
August 29th, 2012
Geometry, Mrs. Sulkes
1-4 Exploration Activity with Angles
Definitions
An angle  is a geometric figure that is made up of two rays that share a common
endpoint. The common endpoint is called the vertex of the angle. The two rays are
called the sides of the angle. You usually name angles with three letters where the vertex
is the middle letter.
C
1.
Name the two rays that make up the given
angle.
2.
Name the vertex of the given angle.
3.
Give two names for the given angle using
the correct symbol.
4.
Draw and label TAN which may have a
degree measure of your choice.
D
E
Naming angles
On occasion, when no confusion results, an angle can be named with just the vertex letter
instead of the usual three letters. Saying B for the left diagram is confusing, but saying
R for the right diagram is clear. Angles can also be named using numbers placed
between the two rays of the angles. You may add numbers to diagrams also.
D
R
A
B
C
E
1
P
Q
Measuring angles
The size of an angle is the smallest amount of rotating necessary to turn one ray to fit
over the other ray of the angle. You measure this rotation in units called degrees. When
you write a lowercase m in from the angle symbol, this indicates the measure of an angle.
For instance, mA  43 .
The protractor is used to measure angles with the following 3 steps:
1. Place the center mark of the protractor on the vertex of the angle.
2. Rotate the zero-edge of the protractor to line up with one side of the angle.
3. Read the size of the angle on the protractor’s scale at the point where the other
side crosses.
Classifying Angles
Angles can be classified into four categories by their measure. Acute angles measure
between 0 and 90 degrees while a right angle measures 90 degrees exactly. An obtuse
angle is one that measures between 90 and 180 degrees while a straight angle is 180
degrees.
Protractor Postulate
Read the Protractor Postulate in your textbook. State two way in which it is similar to the
Ruler Postulate?
1. Apply the Protractor Postulate to find mCOY below.
Y
C
O
A
2. Use the Angle Addition Postulate to write an equation based on the diagram above.
3.
Find the measure of the following angles and classify each angle as acute, right,
obtuse, or straight. Justify you response.
a.
b.
c.
d.
e.
Define the following:
Congruent Angles:
Adjacent Angles:
Bisector of an angle:
Name 5 things that you can assume from a diagram: