Download 1.3: Angles - Angles and Rays

1.3: Angles
- Angles and Rays
GSE
M(G&M)–10–2 Makes and defends conjectures, constructs geometric
arguments, uses geometric properties, or uses theorems to solve
problems involving angles, lines
Rays
• A ray extends forever in one direction
• Has one endpoint
• The endpoint is used first when naming the
ray
B
R
T
W
ray RB
ray WT
Angles
• Angles are formed by 2 non-collinear rays
• The sides of the angle are the two rays
• The vertex is where the two rays meet
Vertex- where they met
ray
ray
Angles (cont.)
• Measured in degrees
• Congruent angles have the same measure
Naming an Angle
You can name an angle by specifying three points: two
on the rays and one at the vertex.
• The angle below may be specified as angle ABC or
ABC. The vertex point is always given in the middle.
Named:
1)Angle ABC
2)Angle CBA
3)Angle B *
Vertex
*you can only use the
vertex if there is ONE
angle
Ex. of naming an angle
• Name the vertex and sides of 4, and give all
possible names for 4.
T
W
4 5
Vertex:
X
X
Sides:
XW & XT
Z
Names:
WXT
TXW
4
Naming angles
Page 35: # 1, 2, 3
Name the angle shown as
Angles can be classified by their measures
• Right Angles – 90 degrees
• Acute Angles – less than 90 degrees
• Obtuse Angles – more than 90, less than 180
Angle Addition Postulate
• If R is in the interior of PQS, then
m PQR + m RQS = m PQS.
P
R
Q
30
20
S
Find the m< CAB
Angle addition postulate – Adding or
subtracting angles
Page 37: #4, 5, 6
Example of Angle Addition Postulate
100
Ans: x+40 + 3x-20 = 8x-60
60
40
4x + 20 = 8x – 60
80 = 4x
20 = x
Angle PRQ = 20+40 = 60
Angle QRS = 3(20) -20 = 40
Angle PRS = 8 (20)-60 = 100
Find the m< BYZ
-2a+48
4a+9
4a+9
In class assignment
Page 38: 1-29, 30-33
Homework:
Practice A (Lesson 1.6)