angles – all you need to know!. contents recap the terms angles in daily life what is an angle?...
TRANSCRIPT
![Page 1: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/1.jpg)
Angles – all you need to know!
![Page 2: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/2.jpg)
Contents• Recap the terms
• Angles in daily life
• What is an angle?
• Naming an angle
• Interior and exterior of an angle
• Measurement of angle
• Types of angle: Right angle
Obtuse angle
Acute angle
Straight angle
• Test Yourself - 1
• Congruent angles
• Pairs of angles: Types
• Test Yourself - 2
• Pairs of angles formed by a transversal
• Test Yourself - 3
![Page 3: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/3.jpg)
PointAn exact location on a plane is called a point.
Line
Line segment
Ray
A straight path on a plane, extending in both directions with no endpoints, is called a line.
A part of a line that has two endpoints and thus has a definite length is called a line segment.
A line segment extended indefinitely in one direction is called a ray.
Recap Geometrical Terms
![Page 4: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/4.jpg)
If we look around us, we will see angles everywhere.
Angles In Daily Life
![Page 5: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/5.jpg)
Common endpoint
B C
B
A
Ray BC
Ray BA
Ray BA and BC are two non-collinear rays
When two non-collinear rays join with a common endpoint (origin) an angle is formed.
What Is An Angle ?
Common endpoint is called the vertex of the angle. B is the vertex of ABC.
Ray BA and ray BC are called the arms of ABC.
![Page 6: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/6.jpg)
Fact: We can also think of an angle formed by rotating one ray away from its initial position.
![Page 7: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/7.jpg)
To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray.
For example: ABC or CBA
We may also name this angle only by the single letter of the vertex, for example B.
A
BC
Naming An Angle
![Page 8: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/8.jpg)
An angle divides the points on the plane into three regions:
A
BC
F
R
P
T
X
Interior And Exterior Of An Angle
• Points lying on the angle (An angle)
• Points within the angle (Its interior portion. )
• Points outside the angle (Its exterior portion. )
![Page 9: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/9.jpg)
Angles are accurately measured in degrees.
Protractor is used to measure and draw angles.
Measurement Of An Angle
![Page 10: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/10.jpg)
There are four main types of angles.
Straight angle
Right angle Acute angle Obtuse angle
A
B C
A
B C
A
B C
BA C
Types Of Angles
![Page 11: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/11.jpg)
Right angle: An angle whose measure is 90 degrees.
Right Angle Acute AngleStraight Angle Obtuse Angle
![Page 12: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/12.jpg)
Examples Of Right Angle
![Page 13: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/13.jpg)
Obtuse angle: An angle whose measure is greater than 90 degrees.
Right Angle Acute AngleStraight Angle Obtuse Angle
![Page 14: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/14.jpg)
Examples Of Obtuse Angle
![Page 15: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/15.jpg)
Acute angle: An angle whose measure is less than 90 degrees.
Right Angle Acute AngleStraight Angle Obtuse Angle
![Page 16: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/16.jpg)
Examples Of Acute Angle
![Page 17: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/17.jpg)
Straight angle: An angle whose measure is 180 degrees.
Right Angle Acute AngleStraight Angle Obtuse Angle
![Page 18: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/18.jpg)
Examples Of Straight Angle
![Page 19: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/19.jpg)
A
BC
D
E F
P
Q R
Which of the angles below is a right angle, less than a right angle and greater than a right angle?
Right angle
Greater than a right angle
Less than a right angle
1. 2.
3.
![Page 20: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/20.jpg)
Using your spiral notebook – write the definitions and draw an example of each of the following angles
![Page 21: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/21.jpg)
Two angles that have the same measure are called congruent angles.
Congruent angles have the same size and shape.
A
BC
300
D
EF
300
D
EF
300
Congruent Angles
![Page 22: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/22.jpg)
Pairs Of Angles : Types
• Adjacent angles
• Vertically opposite angles
• Complementary angles
• Supplementary angles
• Linear pairs of angles
![Page 23: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/23.jpg)
Adjacent AnglesTwo angles that have a common vertex and a common ray are called adjacent angles.
C
D
B
A
Common ray
Common vertex
Adjacent Angles ABD and DBC
Adjacent angles do not overlap each other.
D
EF
A
B
C
ABC and DEF are not adjacent angles
![Page 24: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/24.jpg)
Vertically Opposite AnglesVertically opposite angles are pairs of angles formed by two lines intersecting at a point.
APC = BPD
APB = CPD
A
DB
C
P
Four angles are formed at the point of intersection.
Point of intersection ‘P’ is the common vertex of the four angles.
Vertically opposite angles are congruent.
![Page 25: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/25.jpg)
If the sum of two angles is 900, then they are called complementary angles.
600
A
BC
300
D
EF
ABC and DEF are complementary because
600 + 300 = 900
ABC + DEF
Complementary Angles
![Page 26: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/26.jpg)
700
D
EF
300
p
QR
If the sum of two angles is more than 900 or less than 900, then they not complementary angles.
DEF and PQR are not complementary because
700 + 300 = 1000
DEF + PQR
![Page 27: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/27.jpg)
If the sum of two angles is 1800 then they are called supplementary angles.
PQR and ABC are supplementary, because
1000 + 800 = 1800
RQ
PA
BC
1000 800
PQR + ABC
Supplementary Angles
![Page 28: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/28.jpg)
If the sum of two angles is more than 1800 or less than 1800, then they are not supplementary angles.
DEF and PQR are not supplementary because
ABC + DEF
1100 + 800 = 1900
D
EF
800
CB
A
1100
![Page 29: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/29.jpg)
working with your partner solve the following
![Page 30: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/30.jpg)
![Page 31: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/31.jpg)
Two adjacent supplementary angles are called linear pair of angles.
A
600 1200
PC D
600 + 1200 = 1800
APC + APD
Linear Pair Of Angles
![Page 32: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/32.jpg)
Name the adjacent angles and linear pair of angles in the given figure:
Adjacent angles:
ABD and DBC
ABE and DBA
Linear pair of angles:
EBA, ABC C
D
B
A
E
900
EBD, DBC
C
D
B
A
E
600
30
![Page 33: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/33.jpg)
Name the vertically opposite angles and adjacent angles in the given figure:
A
DB
C
P
Vertically opposite angles: APC and BPD
APB and CPD
Adjacent angles: APC and CPD
APB and BPD
![Page 34: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/34.jpg)
Using your Frayer Template forms write definitions and examples of each of the terms on the next slide
![Page 35: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/35.jpg)
![Page 36: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/36.jpg)
now working with your partner complete the following
![Page 37: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/37.jpg)
Homework for this evening Page 378 Problems 8 through 22 even Show all work – write reasoning if work not
required.
![Page 38: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/38.jpg)
A line that intersects two or more lines at different points is
called a transversal.
Line L (transversal)
BALine M
Line NDC
P
Q
G
F
Pairs Of Angles Formed by a Transversal
Line M and line N are parallel lines.
Line L intersects line M & line N at point P & Q.
Four angles are formed at point P and another four at point
Q by the transversal L.
Eight angles are formed in all by the transversal L.
![Page 39: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/39.jpg)
BALine M
Line NDC
P
Q
G
F
Pairs Of Angles Formed by a Transversal
Can you explain why?
Eight angles are formed in all by the transversal L.
All angles labeled 1 are equal
1
1
1
1
All angles labeled 2 are equal
2
2
2
2
![Page 40: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/40.jpg)
Pairs Of Angles Formed by a Transversal
• Corresponding angles
• Alternate angles
• Interior angles
![Page 41: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/41.jpg)
Corresponding AnglesWhen two parallel lines are cut by a transversal, pairs of corresponding angles are formed.
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.
GPB = PQE
GPA = PQD
BPQ = EQF
APQ = DQF
Line MBA
Line ND E
L
P
Q
G
F
Line L
![Page 42: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/42.jpg)
Alternate AnglesAlternate angles are formed on opposite sides of the transversal and at different intersecting points.
Line MBA
Line ND E
L
P
Q
G
F
Line L
BPQ = DQP
APQ = EQP
Pairs of alternate angles are congruent.
Two pairs of alternate angles are formed.
![Page 43: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/43.jpg)
The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles.
A pair of interior angles lie on the same side of the transversal.
The measures of interior angles in each pair add up to 1800.
Interior Angles
Line MBA
Line ND E
L
P
Q
G
F
Line L
6001200
1200600
BPQ + EQP = 1800
APQ + DQP = 1800
![Page 44: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/44.jpg)
Name the pairs of the following angles formed by a transversal.
Line MBA
Line ND E
P
Q
G
F
Line L
![Page 45: Angles – all you need to know!. Contents Recap the terms Angles in daily life What is an angle? Naming an angle Interior and exterior of an angle Measurement](https://reader035.vdocuments.net/reader035/viewer/2022062309/56649ea05503460f94ba38e1/html5/thumbnails/45.jpg)
Homework
page 384 9 through 24 all
Do not forget to show all work or write reason if work not required.
Begin now please.