Ch. 1-3: Measuring Angles SOL: G4 Objectives: Measure and classify angles. Identify special angle...
-
Upload
stewart-fisher -
Category
Documents
-
view
243 -
download
0
Transcript of Ch. 1-3: Measuring Angles SOL: G4 Objectives: Measure and classify angles. Identify special angle...
Ch. 1-3: Measuring Angles
SOL: G4Objectives:• Measure and classify angles.• Identify special angle pairs.• Use the special angle pairs to find angle measures.
Angle formed by two noncollinear rays that
have a common endpoint.
A
BNoncollinear
rays
Common
EndpointC
A
Sides of an Angle The rays that make the angle
Side AB
Side AC
A
B
C
A
Vertex of an Angle The common endpoint
Vertex A
Symbols When we name an angle, the vertex
point is always in the middle
Note the vertex is the middle point listed
The following are the different ways we can name this angle:
A, BAC, CAB, 4
A
B
C
4
Interior of an Angle Any point inside the angle
Interior
Exterior of an Angle Any point outside the angle
Exterior
Exterior
Equal vs. Congruent
Just like with segments, there is only one way to measure an angle.
To measure an angle, we find how many degrees there are from one side to the other. (360° in a circle)
∠A ≅ ∠C m∠A = m∠C = 70°
A
B
C70° 70°
40°
Example 1:Use the diagram to answer a, b, and c.
a.) Name all angles that have B as a vertex.
b.) Name the sides of 5.
c.) Write another name for 6.
∡ABG, ∡ABD, ∡DBE or ∡DBF,
∡EBG or ∡FBG, ∡5, ∡6, ∡7
BG and BE or BF
∡DBE or ∡DBF
Measuring AnglesTo measure an angle, you use a protractor.
The protractor has two scalesrunning from 0 to 180 degrees
in opposite directions. These are the scales we use to determine the
measure of the angle
Place the center point of theprotractor on the vertex
Align the 0 on either sideof the scale with one side
of the angle. (Paying attention to which
direction the angle is opening
Example 2:Find the measure of PQR.
P Q
R
Since QP is aligned with the 0on the outer scale, use the outer scale to find that QR intersects
the scale at 65 degrees.
65°
Classify Angles by Angle Measure
Measures 90 Written as mA = 90
Right Angle
Acute Angle
This symbol means, right
angle, perpendicular
A B
Measures less than 90
Written as mB < 90
Obtuse Angle Straight Angle (Line)
Measures greater than 90
Written as mC > 90
C
A B C
Classify Angles by Angle Measure
Measures 180
Angle Bisector
An angle bisector is a segment, line, or ray that splits an angle into two congruent angles.
In the picture, rayBD bisects ∠ABC. Therefore, we know∠ABD ≅ ∠DBC.
Postulate 1.8: Angle Addition Postulate If point B is in the interior of ∠AOC , then
m∠AOB + m∠BOC = m∠AOC
Example 6:Apply the angle addition postulate.
A
D
C
B
23°
41°
What is the m∡ABC?
E
H
G
F
If m∠EFG = 23°, what is the m∠EFH?
11°If m∠KJL = 117°,
what is the m∠KJM?
K
M
L
J
68°
m∡ABD + m∡CBD = m∡ABC23° + 41° =
64°
64°
12°m∡EFG - m∡GFH =
m∡EFH23° - 11° = 12°
49°m∡KJL - m∡LJM = m∡KJM
117° - 68° = 49°
Example 7: If m∠RQT = 155°, what are the m∠RQS and m∠SQT?
m∡RQS + m∡TQS = m∡RQT
(4x – 20) + (3x + 14) = 155°
7x – 6= 155°+ 6 + 6
7x = 161°
7x = 161°7 7x = 23
m∡RQS = 4x – 20 = 4(23) – 20 = 72°m∡TQS = 3x + 14 = 3(23) + 14 = 83°
Check:72° + 83° =
155°