1.4 – measure and classify angles & angle constructions
DESCRIPTION
1.4 – Measure and Classify Angles & Angle Constructions. 1.5 –Describe Angle Pair Relationships. B. 1. A. C. Two different rays with the same initial point. Measured in degrees. Angle:. A ,. BAC ,. CAB,. 1. B. A. C. B. A. C. Common initial point, where rays meet. - PowerPoint PPT PresentationTRANSCRIPT
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1.4 – Measure and Classify Angles &Angle Constructions
1.5 –Describe Angle Pair Relationships
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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
AC
B
AC
B
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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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Angle Bisector
Ray that cuts an angle in half to make 2 congruent angles
P
Q R
S
QS bisects PQR
PQS SQR
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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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Complementary Angles: Two angles that add to 90°
m1 + m2 = 90°
12
1
2
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Supplementary Angles: Two angles that add to 180°
m1 + m2 = 180°
1 21
2
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Linear Pair: Supplementary angles that are adjacent
1 2
m1 + m2 = 180°
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Vertical Angles: Two angles whose sides form two pairs of opposite rays
12
They will always be congruent!
21
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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
Pt. E ED
EF
Names Vertex Sides
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1. Give three names for the angle shown, then name the vertex and sides.
QVS
SVQ
V
Pt. V VQ
VS
Names Vertex Sides
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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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5. Find each indicated angle.
15°
15°
75° 90°
90°
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5. 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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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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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 =
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8. Tell whether the indicated angles are adjacent.
EFG and HGF
no
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8. Tell whether the indicated angles are adjacent.
JNM and MNK
yes
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9. Name a pair of complementary angles, supplementary angles, and vertical angles .
Complementary:QOR and ROL
Supplementary:ROL and LON
ROM and MON
Vertical:
L
M
N
PQ
R OMON and NOP
QOL and LOM
ROL and NOP
LOM and QOP
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9. Name a pair of complementary angles, supplementary angles, and vertical angles .
Complementary:DGE and EGA
Supplementary:DGE and EGB
DGA and AGB
Vertical:
EGA and AGC
DGE and BGC
EGB and DGCA
B
C
D
E
G
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10. 1 and 2 are complementary angles. Given the measure of 1, find m2.
m1 = 82°
m2 = 8°90 – 82 =
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10. 1 and 2 are complementary angles. Given the measure of 1, find m2.
m2 = 67°90 – 23 =
m1 = 23°
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11. 1 and 2 are supplementary angles. Given the measure of 1, find m2.
m2 = 98°180 – 82 =
m1 = 82°
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m2 = 75°180 – 105 =
m1 = 105°
11. 1 and 2 are supplementary angles. Given the measure of 1, find m2.
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12. Find the measure of ABD and DBC.
4x + 6 + 11x – 6 = 180
15x = 180x = 12
mABD = 4(12)+6= 48+6= 54°
mDBC = 11(12)-6= 132-6= 126°
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12. Find the measure of ABD and DBC.
2x + 3x = 90
5x = 90x = 18
mABD = 2(18)= 36°
mDBC = 3(18)= 54°
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13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
1 and 2
Linear pair
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13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
2 and 4
Vertical angles
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6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
5 and 8
neither
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7. Find the values of x and y.
6x – 11 + 2x – 9 = 180
8x – 20 = 180 8x = 200
x = 25°
20y + 19 + 2x – 9 = 18020y + 19 + 2(25) – 9 = 180
20y + 60 = 180
20y = 120y = 6°
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7. Find the values of x and y.
9x + 2 + 10x + 7 = 180
19x + 9 = 18019x = 171
x = 9°
18y + 25 + 9x + 2 = 180
18y + 25 + 9(9) + 2 = 180
18y + 108 = 180
18y = 72y = 4°
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HW Problem
1.4 # 38
1.41.5
28-3238-41
4-18 even, 21, 22, 24-27, 33-38 (draw pic), 40, 414, 5, 7-33 odd, 49-52, 61, 62
**Bring compass and ruler tomorrow! Books will not be needed
53°
37°