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Geometry Chapter 1

Geometry Chapter 1. Section 1-4 Measuring Angles. 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.

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Geometry Chapter 1

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  1. Geometry Chapter 1 Section 1-4 Measuring Angles

  2. 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

  3. Ray BAand rayBCare called the sides of ÐABC. What Is An Angle ? B C A When two non-collinear rays join with a common endpoint (origin) an angle is formed. Ray BA B Common endpoint Ray BC Common endpoint is called the vertex of the angle.Bis thevertexof ÐABC. Ray BA and BC are two non-collinear rays

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

  5. A Naming An Angle To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. B C 1 For example: ÐABC or ÐCBA We may also name this angle only by the single letter of the vertex, for example ÐB or by a number.

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

  7. Measurement Of An Angle One way to measure and angle is in degrees. To indicate the size or degree of an angle write a lower case m in front of the angle symbol. The measure of angle B is 65 degrees You show this by writing m<B = 65. A B C

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

  9. Types Of Angles C A B A A A There are four main types of angles. B B B Right angle Acute angle Obtuse angle C C C Straight angle

  10. Straight Angle Obtuse Angle Acute Angle Right Angle Right angle: An angle whose measure is 90 degrees.

  11. Examples Of Right Angle

  12. Straight Angle Obtuse Angle Acute Angle Right Angle Obtuse angle: An angle whose measure is greater than 90 degrees.

  13. Examples Of Obtuse Angle

  14. Straight Angle Obtuse Angle Acute Angle Right Angle Acute angle: An angle whose measure is less than 90 degrees.

  15. Examples Of Acute Angle

  16. Straight Angle Obtuse Angle Acute Angle Right Angle Straight angle: An angle whose measure is 180 degrees.

  17. Examples Of Straight Angle

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

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

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

  21. D Adjacent Angles A C A Two angles that have acommon vertexand acommon rayare called adjacent angles. E D B F Common ray B C Common vertex Adjacent AnglesÐABDand ÐDBC ÐABCand ÐDEF are not adjacent angles Adjacent angles do not overlap each other.

  22. 600 1200 D Linear Pair Of Angles C A Two adjacent supplementary angles are called linear pair of angles. P ÐAPC + ÐAPD 600 + 1200 = 1800

  23. Vertical Angle Pairs Vertical Angles: two angles whose sides are opposite rays. 1 2 4 3 Name the pairs of vertical angles. ∠1 and ∠3 ∠4 and ∠2

  24. Pairs Of Angles : Types • Complimentary angles • Supplementary angles

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

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

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

  28. Contd…. D A If the sum of two angles ismore than 1800orless than 1800, then they arenot supplementary angles. 1100 800 E B F C ÐDEFandÐPQRarenot supplementarybecause ÐABC + ÐDEF 1100 + 800 = 1900

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

  30. Pairs Of Angles Your Turn Complete problems on Page 72-73 #18 -25

  31. The End Modified by Mrs. D. Joseph Excerpts The Department of Research Bombay Cambridge Gurukul

  32. Contents • Recap the terms • Test Yourself - 1 • Angles in daily life • Congruent angles • Pairs of angles: Types • What is an angle? • Test Yourself - 2 • Naming an angle • Pairs of angles formed by a transversal • Interior and exterior of an angle • Test Yourself - 3 • Measurement of angle • Types of angle: Right angle • Obtuse angle • Acute angle • Straight angle

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