angles grade 7 the shape of design. point an exact location on a plane is called a point. line line...
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Angles
Grade 7
The Shape of Design
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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
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If we look around us, we will see angles everywhere.
Angles In Daily Life
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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.
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Fact: We can also think of an angle formed by rotating one ray away from its initial position.
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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
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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. )
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Angles are accurately measured in degrees.
Protractor is used to measure and draw angles.
Measurement Of An Angle
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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
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Right angle: An angle whose measure is 90 degrees.
Right Angle Acute AngleStraight Angle Obtuse Angle
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Examples Of Right Angle
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Obtuse angle: An angle whose measure is greater than 90 degrees.
Right Angle Acute AngleStraight Angle Obtuse Angle
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Examples Of Obtuse Angle
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Acute angle: An angle whose measure is less than 90 degrees.
Right Angle Acute AngleStraight Angle Obtuse Angle
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Examples Of Acute Angle
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Straight angle: An angle whose measure is 180 degrees.
Right Angle Acute AngleStraight Angle Obtuse Angle
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Examples Of Straight Angle
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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.
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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
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Pairs Of Angles : Types
• Adjacent angles
• Complimentary angles
• Supplementary angles
• Linear pairs of angles
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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
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If the sum of two angles is 900, then they are called complimentary angles.
600
A
BC
300
D
EF
ABC and DEF are complimentary because
600 + 300 = 900
ABC + DEF
Complimentary Angles
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700
D
EF
300
p
QR
If the sum of two angles is more than 900 or less than 900, then they not complimentary angles.
DEF and PQR are not complimentary because
700 + 300 = 1000
DEF + PQR
Contd….
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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
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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
Contd….
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Two adjacent supplementary angles are called linear pair of angles.
A
600 1200
PC D
600 + 1200 = 1800
APC + APD
Linear Pair Of Angles
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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
600
300
900
EBD, DBC
C
D
B
A
E
600
300
900