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Angles Grade 7 The Shape of Design. Point An exact location on a plane is called a point. Line Line segment Ray A straight path on a plane, extending.

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Presentation on theme: "Angles Grade 7 The Shape of Design. Point An exact location on a plane is called a point. Line Line segment Ray A straight path on a plane, extending."— Presentation transcript:

1 Angles Grade 7 The Shape of Design

2 Point An 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

3 If we look around us, we will see angles everywhere. Angles In Daily Life

4 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.

5 Fact: We can also think of an angle formed by rotating one ray away from its initial position.

6 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 B C Naming An Angle

7 An angle divides the points on the plane into three regions: A B C 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. )

8 Angles are accurately measured in degrees. Protractor is used to measure and draw angles. Measurement Of An Angle

9 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

10 Right angle: An angle whose measure is 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle

11 Examples Of Right Angle

12 Obtuse angle: An angle whose measure is greater than 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle

13 Examples Of Obtuse Angle

14 Acute angle: An angle whose measure is less than 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle

15 Examples Of Acute Angle

16 Straight angle: An angle whose measure is 180 degrees. Right AngleAcute AngleStraight AngleObtuse Angle

17 Examples Of Straight Angle

18 A B C 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

19 Two angles that have the same measure are called congruent angles. Congruent angles have the same size and shape. A B C 30 0 D E F D E F Congruent Angles

20 Pairs Of Angles : Types Adjacent angles Complimentary angles Supplementary angles Linear pairs of angles

21 Adjacent Angles Two 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 E F A B C ABC and DEF are not adjacent angles

22 If the sum of two angles is 90 0, then they are called complimentary angles A B C 30 0 D E F ABC and DEF are complimentary because = 90 0 ABC + DEF Complimentary Angles

23 70 0 D E F 30 0 p Q R If the sum of two angles is more than 90 0 or less than 90 0, then they not complimentary angles. DEF and PQR are not complimentary because = DEF + PQR Contd….

24 If the sum of two angles is then they are called supplementary angles. PQR and ABC are supplementary, because = R Q P A B C PQR + ABC Supplementary Angles

25 If the sum of two angles is more than or less than 180 0, then they are not supplementary angles. DEF and PQR are not supplementary because ABC + DEF = D E F 80 0 C B A Contd….

26 Two adjacent supplementary angles are called linear pair of angles. A P C D = APC + APD Linear Pair Of Angles

27 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 EBD, DBC C D B A E


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