Transcript Geometry 1-3

Geometry 1-3
Measuring and Constructing
Angles
Vocabulary
• Angle- a figure formed by two rays, or
sides, with a common endpoint.
• Vertex- The common endpoint of an angle
(plural: vertices).
• Interior of an angle- all points between the
sides of an angle.
• Exterior of an angle- all points outside of
the sides of an angle.
• Degree- the unit of measure for angles.
Naming Angles
•
Angles can be named three ways:
1. By its vertex
R
2. By a number 1
3. By a point on each ray and the vertex
SRT or
TRS
S
R
1
T
Name the Marked Angle
W
2
A
R
L
Types of Angles
• Acute angle: 1° to 89 °
• Right angle: 90 °
• Obtuse angle: 91 ° to 179 °
• Straight angle: 180 °
More Vocab.
• Congruent angles- angles that have the
same measure.
• Angle bisector- A ray that divides an angle
into two congruent angles
W
A
Congruent angles:
ARW  LRW
Angle bisector: RW
45°
45°
R
L
Postulate
• Angle Addition Postulate:
If S is in the interior of PQR, then
m PQS + m SQR = m PQR
(part 1 + part 2 = the whole)
R
S
Q
P
Example
• What is the measure of angle WRL?
T
A
W
65°
45°
R
L
Example
• If Y is in the interior of LMN, find the
m LMY if m LMY = 5x+3, m YMN = 3x+3,
and m LMN=86°.
Using a Protractor
wxv
YXZ
zxw