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Angles Grade 7 The Shape of Design

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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

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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 B C Naming An Angle

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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. )

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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 AngleAcute AngleStraight AngleObtuse 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 AngleAcute AngleStraight AngleObtuse 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 AngleAcute AngleStraight AngleObtuse Angle

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Examples Of Acute Angle

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

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Examples Of Straight Angle

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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

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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

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

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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

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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

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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….

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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

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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….

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Two adjacent supplementary angles are called linear pair of angles. A P C D = 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 EBD, DBC C D B A E

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