Transcript 1.4 PowerPoint

1.4 –Measure and Classify Angles &
Angle Constructions
Angle: Two different rays with the same initial
point. Measured in degrees.
B
A
1
C
A, BAC, CAB, 1
Common initial
Vertex point, where
rays meet
pt. A
vertex
side
Sides
AB
The rays of
the angle
AC
side
Interior
Point
Point
inside an
angle
D
Point
Exterior outside an
Point
angle
E
Pt. D is in
the interior
of BAC
Pt. E is in
the exterior
of BAC
Acute
Right
Angle more
than 0°, but
less than 90°
Angle that
measures 90°
Obtuse
Angle more
than 90°, but
less than 180°
Straight
Angle that
measures 180°
mA = 50°
A
mR = 90°
R
mO = 110°
O
S
mS = 180°
Angle Bisector: Ray that cuts an angle in half to
make 2 congruent angles
P
QS bisects PQR
S
PQS  SQR
mPQS = mSQR
Q
R
Note: To name an angle use “  ”, but when
m
stating its measure use “_______”.
Adjacent angles: Two angles that share a
common side and vertex
2 1
1 is adjacent to 2
Angle Addition Postulate:
If you add two adjacent angles, it totals to get
their sum.
C
A
B
D
mABC + mCBD = mABD
1. Give three names for the angle shown, then name the
vertex and sides.
DEF
FED
E
Vertex
Pt. E
Sides
ED
EF
1. Give three names for the angle shown, then name the
vertex and sides.
QVS
SVQ
V
Vertex
Pt. V
Sides
VQ
VS
2. Classify the angle as acute, right, obtuse or straight.
mA = 115°
obtuse
2. Classify the angle as acute, right, obtuse or straight.
mA = 90°
right
2. Classify the angle as acute, right, obtuse or straight.
mA = 85°
acute
2. Classify the angle as acute, right, obtuse or straight.
mA = 180°
straight
3. Use a protractor to find the measure of the angle to
the nearest degree. Then classify the angle as acute,
obtuse, straight, or right.
91°
obtuse
3. Use a protractor to find the measure of the angle to
the nearest degree. Then classify the angle as acute,
obtuse, straight, or right.
32°
acute
3. Use a protractor to find the measure of the angle to
the nearest degree. Then classify the angle as acute,
obtuse, straight, or right.
180°
straight
4. Find the indicated measure.
mPRS = 81+42
mPRS = 123°
4. Find the indicated measure.
mWXZ = 90 – 26 =
mWXZ = 64°
mNRP + mPRQ = mNRQ
8x + 7 + 4x – 1 = 78
12x + 6 = 78
12x = 72
x=6
mPRQ = 4(6) – 1
mPRQ = 24 – 1
mPRQ = 23°
mADB + mBDC = mADC
11x – 7 + 5x – 3 = 118
16x – 10 = 118
16x = 128
x=8
mADB = 11(8) – 7
mADB = 88 – 7
mADB = 81°
Find each indicated angle.
20°
15°
a = 180-160 = 20°
b = 180-20 = 160°
160°
c = 180-90-75 = 15°
d = 180-90-15 = 75°
Find each indicated angle.
67°
106°
74°
157°
a = 180-74 = 106°
b = 180-106 = 74°
c = 180-90-23 = 67°
d = 180-23 = 157°
mJKM = 51°
51°
mJKL = 102°
mJKM = 39.5°
mJKL = 79°
39.5°
5x + 2 = 7x – 6
2 = 2x – 6
8 = 2x
4=x
mABC = 5(4)+2 + 7(4)-6 = 20+2 +28-6 = 44°
5x + 13 = 9x – 23
13 = 4x – 23
36 = 4x
9=x
mABC = 5(9)+13 + 9(9)-23 = 45+13+81-23 = 116°
HW Problem
1.4 28-32 1-5 odd, 6-20 even, 21, 22, 24-27, 30,
33-38 (draw pic), 40, 41
# 38
53°
37°
**Bring compass and ruler tomorrow!
Books will not be needed