1.4 –measure and classify angles & angle constructions
DESCRIPTION
1.4 –Measure and Classify Angles & Angle Constructions. B. 1. A. C. Two different rays with the same initial point. Measured in degrees. Angle:. A ,. BAC ,. CAB,. 1. Common initial point, where rays meet. pt. A. vertex. side. The rays of the angle. side. - PowerPoint PPT PresentationTRANSCRIPT
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1.4 –Measure and Classify Angles &Angle Constructions
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Angle: Two different rays with the same initial point. Measured in degrees.
A, BAC, CAB, 1
B
A1
C
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Vertex
Sides
Common initial point, where rays meet
The rays of the angle
vertex
pt. A
side
side
AB
AC
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Interior Point
Exterior Point
Point inside an angle
D Pt. D is in the interior of BAC
Point outside an angle
E
Pt. E is in the exterior of BAC
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Acute
Right
Obtuse
Straight
Angle more than 0°, but less than 90°
Angle more than 90°, but less than 180°
Angle that measures 90°
Angle that measures 180°
AmA = 50°
RmR = 90°
OmO = 110°
SmS = 180°
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Ray that cuts an angle in half to make 2 congruent angles
QS bisects PQR
PQS SQR
Angle Bisector:
P
Q R
S
mPQS = mSQR
Note: To name an angle use “ ”, but when
stating its measure use “_______”.m
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Adjacent angles: Two angles that share a common side and vertex
12
1 is adjacent to 2
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Angle Addition Postulate:
If you add two adjacent angles, it totals to get their sum.
A
B
C
D
mABC + mCBD = mABD
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1. Give three names for the angle shown, then name the vertex and sides.
DEF
FED
E
Vertex Sides
Pt. E ED
EF
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1. Give three names for the angle shown, then name the vertex and sides.
QVS
SVQ
V
Vertex Sides
Pt. V VQ
VS
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2. Classify the angle as acute, right, obtuse or straight.
mA = 115°
obtuse
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2. Classify the angle as acute, right, obtuse or straight.
mA = 90°
right
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2. Classify the angle as acute, right, obtuse or straight.
mA = 85°
acute
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2. Classify the angle as acute, right, obtuse or straight.
mA = 180°
straight
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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
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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
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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
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4. Find the indicated measure.
mPRS = 81+42
mPRS = 123°
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4. Find the indicated measure.
mWXZ = 90 – 26 =
mWXZ = 64°
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mNRP + mPRQ = mNRQ 8x + 7 + 4x – 1 = 78
12x + 6 = 7812x = 72
x = 6
mPRQ = 4(6) – 1
mPRQ = 24 – 1mPRQ = 23°
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mADB + mBDC = mADC 11x – 7 + 5x – 3 = 118
16x – 10 = 11816x = 128
x = 8
mADB = 11(8) – 7
mADB = 88 – 7mADB = 81°
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Find each indicated angle.
a = 180-160 = 20°
20°
b = 180-20 = 160°
160°
c = 180-90-75 = 15°
d = 180-90-15 = 75°
15°
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Find each indicated angle.
a = 180-74 = 106°
b = 180-106 = 74°
c = 180-90-23 = 67°
d = 180-23 = 157°
74°
106°67°
157°
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51°
51°mJKM =
102°mJKL =
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39.5°mJKM =
79°mJKL =
39.5°
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mABC =
5x + 2 = 7x – 6
2 = 2x – 6
8 = 2x4 = x
44°5(4)+2 + 7(4)-6 = 20+2 +28-6 =
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5x + 13 = 9x – 23
13 = 4x – 23
36 = 4x9 = x
mABC = 116°5(9)+13 + 9(9)-23 = 45+13+81-23 =