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**Grade 7 The Shape of Design**

Angles Grade 7 The Shape of Design

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**Recap Geometrical Terms**

An exact location on a plane is called a point. Point A straight path on a plane, extending in both directions with no endpoints, is called a line. Line A part of a line that has two endpoints and thus has a definite length is called a line segment. Line segment A line segment extended indefinitely in one direction is called a ray. Ray

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**If we look around us, we will see angles everywhere.**

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

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**Ray BA and BC are two non-collinear rays**

What Is An Angle ? When two non-collinear rays join with a common endpoint (origin) an angle is formed. A Ray BA B Common endpoint B C Ray BC Common endpoint is called the vertex of the angle. B is the vertex of ÐABC. Ray BA and BC are two non-collinear rays 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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**Naming An Angle A B C For example: ÐABC or ÐCBA**

To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. A B C For example: ÐABC or ÐCBA We may also name this angle only by the single letter of the vertex, for example ÐB.

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**Interior And Exterior Of An Angle**

An angle divides the points on the plane into three regions: Points lying on the angle (An angle) A B C P T X F R Points within the angle (Its interior portion. ) Points outside the angle (Its exterior portion. )

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**Measurement Of An Angle Protractor is used to measure and draw angles.**

Angles are accurately measured in degrees.

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**There are four main types of angles.**

Right angle Acute angle Obtuse angle A B C A B C A B C Straight angle B A C

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**Right angle: An angle whose measure is 90 degrees.**

Straight Angle Right Angle Acute 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.**

Straight Angle Right Angle Acute 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.**

Straight Angle Right Angle Acute 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 Angle Obtuse Angle

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**Examples Of Straight Angle**

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**Greater than a right angle**

Which of the angles below is a right angle, less than a right angle and greater than a right angle? 1. D E F 2. P Q R Test Yourself 1 Greater than a right angle A B C Right angle 3. Less than a right angle

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**Congruent Angles A B C D E F D E F**

Two angles that have the same measure are called congruent angles. A B C 300 D E F 300 D E F 300 Congruent angles have the same size and shape.

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**Pairs Of Angles : Types Adjacent angles Complimentary angles**

Supplementary angles Linear pairs of angles

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**Adjacent Angles ABC and DEF are not 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 D E F A B C Adjacent Angles ABD and DBC ABC and DEF are not adjacent angles Adjacent angles do not overlap each other.

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**ÐABC and ÐDEF are complimentary because**

Complimentary Angles If the sum of two angles is 900, then they are called complimentary angles. 600 A B C 300 D E F ÐABC and ÐDEF are complimentary because ÐABC + ÐDEF = 900

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**ÐDEF and ÐPQR are not complimentary because**

Contd…. If the sum of two angles is more than 900 or less than 900, then they not complimentary angles. 700 D E F 300 p Q R ÐDEF and ÐPQR are not complimentary because ÐDEF + ÐPQR = 1000

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**ÐPQR and ÐABC are supplementary, because**

Supplementary Angles If the sum of two angles is 1800 then they are called supplementary angles. R Q P A B C 1000 800 ÐPQR and ÐABC are supplementary, because ÐPQR + ÐABC = 1800

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**ÐDEF and ÐPQR are not supplementary because**

Contd…. If the sum of two angles is more than or less than 1800, then they are not supplementary angles. C B A 1100 D E F 800 ÐDEF and ÐPQR are not supplementary because ÐABC + ÐDEF = 1900

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**Two adjacent supplementary angles are called linear pair of angles.**

1200 600 C D P ÐAPC + ÐAPD = 1800

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**ÐABD and ÐDBC Test Yourself 2 ÐABE and ÐDBA ÐEBA, ÐABC ÐEBD, ÐDBC**

Name the adjacent angles and linear pair of angles in the given figure: Adjacent angles: C D B A E 600 300 900 C D B A E 600 300 900 ÐABD and ÐDBC ÐABE and ÐDBA Test Yourself 2 Linear pair of angles: ÐEBA, ÐABC ÐEBD, ÐDBC

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