1. Angles (right, acute, obtuse) protractor
Grade 4
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Let’s warm up :
Classify each pair of lines as parallel, intersecting, or perpendicular. 1 2 3 4
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3. Let’s review what we did in the last session
Parallel lines
Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. l m
Lines m and l are parallel lines.
They will travel to infinity in either direction and never intersect.
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4. Review
Intersecting lines
Two or more lines that meet at a point are called intersecting lines. That point would be on each of these lines. x Q y
In the Figure, lines x and y are intersecting lines and intersect at point Q.
Lines can only intersect at one point and only one point.
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Review
Perpendicular lines.
If the line segments meet or cross each other to form square corners, they are perpendicular to each other. s
right angles t
The little box drawn in the corner, means "at right angles“.
Perpendicular lines intersect at a point and form 4 right angles.
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Review
What is the difference between perpendicular and parallel?
90 degrees (a right angle)
If you rotate a perpendicular line by 90° it will become parallel (but not if it touches!), and the other way around.
perpendicular lines
rotate
parallel
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7. Symbols in Geometry || Here are the some geometrical symbols: Symbol
Review
Symbols in Geometry
Here are the some geometrical symbols:
Symbol
Meaning
Example
In Words ||
parallel
EF||GH
The line EF is parallel to line GH
perpendicular
AB CD
The line AB is perpendicular to line CD
Right angle
is 90°
A right angle is 90 degrees
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8. Angles (right, acute, obtuse) protractor
Let’s start with
Angles (right, acute, obtuse) protractor
What Is an Angle?
An angle is a combination of two rays with a common endpoint. B
angle AOB
vertex O A
arm
The endpoint (O) is known as the vertex of the angle
And
the rays (OA and OB) are called the sides or arms of the angle .
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Labeling Angles
There are two main ways to label angles: A
1) By giving the angle a name, usually a lower-case letter like a or b, or sometimes a Greek letter like α (alpha) or θ (theta). a C B θ
2) Or by the three letters on the shape that define the angle, with the middle letter being where the angle actually is (its vertex). D
Here, angle "a" is "BAC", and angle "θ" is "BCD"
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10. We use a little circle ° following the number to mean degrees.
Measurement of Angles
We use a little circle ° following the number to mean degrees.
For example: 45° means 45 degrees.
There are 360 degrees in one Full Rotation (one complete circle around).
Half a circle is 180°.
Quarter of a circle is 90° .
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11. Measuring angles in Degrees
We often measure degrees using a protractor.
The normal protractor measures 0° to 180°.
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12. Types of Angles As the angle increases, the name of the angle Changes.
The angle classification is summarized as follows:
Type of Angle
Description
Acute angle
An angle that is less than 90°
Right angle
An angle that is 90° exactly
Obtuse angle
An angle that is greater than 90° but less than 180°
Straight angle
An angle that is 180° exactly
Reflex angle
An angle that is greater than 180°
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13. Angles On a Straight Line
Angles on one side of a straight line will always add to 180 degrees.
If a line is split into 2 and you know one angle you can always find the other one.
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14. If we know one angle is 45°, what is angle “x" ?
Angle x will be 180° − 45° = 135°
This method can be used to find angles on one side of a straight line.
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15. Angles Around a Point
Angles around a point will always add up to 360 degrees.
110°
40°
60°
150°
The angles here all add to 360°.
40° + 110° + 150° + 60° = 360°
Because of this, if there is an unknown angle we can always find it.
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16. Complementary Angles
Two Angles are Complementary if they add up to 90 degrees (a Right Angle).
60°
30°
These two angles (40° and 50°) are Complementary Angles, because they add up to 90°.
But the angles don't have to be together to Complement each other.
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17. Supplementary Angles
Two Angles are Supplementary if they add up to 180 degrees (a Straight Angle).
120°
60°
These two angles (120° and 60°) are Supplementary Angles, because they add up to 180°.
But the angles don't have to be together to Supplement each other.
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BREAK
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20. Assignments Find the missing angle: ? 1 2 40° ? 60° 150° 3 ? 55° 130°
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21. Find the Complement of the following:4 ? 5
61°
25° ? 6 ?
27°
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22. Find the Supplement of the following:7 8
125°
110° ? ? 9 ?
45°
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23. Find the missing angle around a point:
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24. Very Good!
Let's Review
What Is an Angle?
An angle is a combination of two rays with a common endpoint. B
angle AOB
vertex O A
arm
The endpoint (O) is known as the vertex of the angle
And
the rays (OA and OB) are called the sides or arms of the angle .
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25. Measuring angles in Degrees
Review
Measuring angles in Degrees
We often measure degrees using a protractor.
The normal protractor measures 0° to 180°.
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26. Angles On a Straight Line
Review
Angles On a Straight Line
If we know one angle is 45°, what is angle “x" ? x
45°
Angle x will be 180° − 45° = 135°
This method can be used to find angles on one side of a straight line.
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27. Review
Angles Around a Point
Angles around a point will always add up to 360 degrees.
110°
40°
60°
150°
The angles here all add to 360°.
40° + 110° + 150° + 60° = 360°
Because of this, if there is an unknown angle we can always find it.
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28. Review
Complementary Angles
Two Angles are Complementary if they add up to 90 degrees (a Right Angle).
60°
30°
These two angles (40° and 50°) are Complementary Angles, because they add up to 90°.
But the angles don't have to be together to Complement each other.
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29. Review
Supplementary Angles
Two Angles are Supplementary if they add up to 180 degrees (a Straight Angle).
120°
60°
These two angles (120° and 60°) are Supplementary Angles, because they add up to 180°.
But the angles don't have to be together to Supplement each other.
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30. Remember to do the practice worksheets!!!
You have done a nice job.
Remember to do the practice worksheets!!!
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