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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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Angles Review. This powerpoint presentation will allow you to work at your own pace through various angle problems.

Angles Review. This powerpoint presentation will allow you to work at your own pace through various angle problems.

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