1 / 37

Angles, lines, rays, and segments

Angles, lines, rays, and segments. MATHEMATICS. 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.

kata
Download Presentation

Angles, lines, rays, and segments

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Angles, lines, rays, and segments MATHEMATICS

  2. 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

  3. 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

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

  5. A B C Ray BAand rayBCare called thearmsof ABC. What Is An Angle ? 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

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

  7. A B C 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. For example: ÐABC or ÐCBA We may also name this angle only by the single letter of the vertex, for example ÐB.

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

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

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

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

  12. Examples Of Right Angle

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

  14. Examples Of Obtuse Angle

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

  16. Examples Of Acute Angle

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

  18. Examples Of Straight Angle

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

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

  21. Pairs Of Angles : Types • Adjacent angles • Vertically opposite angles • Complimentary angles • Supplementary angles • Linear pairs of angles

  22. A D A C D Common ray B E F B C Common vertex Adjacent Angles Two angles that have acommon vertexand acommon rayare called adjacent angles. Adjacent AnglesABDand DBC ABCand DEF are not adjacent angles Adjacent angles do not overlap each other.

  23. A C D B Vertically Opposite Angles Vertically opposite angles are pairs of angles formed bytwo lines intersecting at a point. ÐAPC = ÐBPD ÐAPB = ÐCPD P Four anglesare formed at the point of intersection. Vertically opposite angles arecongruent. Point of intersection ‘P’ is thecommon vertex of the four angles.

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

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

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

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

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

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

  30. C A P D B Name the vertically opposite angles and adjacent angles in the given figure: Vertically opposite angles: ÐAPC and ÐBPD Adjacent angles:ÐAPC and ÐCPD ÐAPB and ÐCPD ÐAPB and ÐBPD

  31. G B A C D F Pairs Of Angles Formed by a Transversal A line that intersects two or more lines at different points is called a transversal. Line L (transversal) Line M P Line N Q Four angles are formed at point P and another four at point Q by the transversal L. Line M and line N are parallel lines. Line L intersects line M and line N at point P and Q. Eight angles are formed in all by the transversal L.

  32. Pairs Of Angles Formed by a Transversal • Corresponding angles • Alternate angles • Interior angles

  33. L Line L G Line M P A B Line N Q D E F Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent.

  34. L Line L G Line M P A B Line N Q D E F Alternate Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. ÐBPQ = ÐDQP ÐAPQ = ÐEQP Two pairs of alternate angles are formed. Pairs of alternate angles are congruent.

  35. L Line L G Line M P A B Line N Q D E F Interior Angles The angles that lie in the area between the two parallel lines that are cut by a transversal, are calledinterior angles. ÐBPQ + ÐEQP = 1800 600 1200 1200 600 ÐAPQ + ÐDQP = 1800 The measures of interior angles in each pairadd up to 1800. A pair of interior angles lie on thesame sideof the transversal.

  36. Line L G Line M P A B 500 Line L G 1300 Line M Line N A P B Q E D Line L G F Line N Q D E Line M P A B F Line N Q E D F Name the pairs of the following angles formed by a transversal. Test Yourself 3 Corresponding angles Alternate angles Interior angles

  37. The End

More Related