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Geometry

Geometry. Take out: Binder, Pencil, Do Now Sheet, Homework. Do Now: Name each figure 1) 2) 3) Draw a line AD with a midpoint C, then write all congruent segment using correct notation. B. A. Agenda Do Now/Check Homework HW Questions Naming, Measuring, and Drawing Angles

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Geometry

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  1. Geometry • Take out: Binder, Pencil, Do Now Sheet, Homework Do Now: Name each figure 1) 2) 3) Draw a line AD with a midpoint C, then write all congruent segment using correct notation. B A • Agenda • Do Now/Check Homework • HW Questions • Naming, Measuring, and Drawing Angles • Angles and Protractor Practice • Ticket-to-go • HW: pg. 42-44 #’s 1-4, 7-14, 34 F E 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  3. Angles In Daily Life If we look around us, we will see angles everywhere. 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  4. 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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  5. Fact: We can also think of an angle formed by rotating one ray away from its initial position. 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  6. 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. 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  7. Measurement Of An Angle Protractor is used to measure and draw angles. Angles are accuratelymeasured in degrees. 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  8. B A A A B B C B C A C C Types Of Angles There are four main types of angles. Right angle Acute angle Obtuse angle Straight angle 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  9. Right angle: An angle whose measure is 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  10. Obtuse angle: An angle whose measure is greater than 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  11. Acute angle: An angle whose measure is less than 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  12. Straight angle: An angle whose measure is 180 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  13. Examples Of Straight Angle 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  14. 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. 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  15. A B C Angle Bisectors A ray that begins at the angles vertex and divides the angle into two congruent angles. D Ray BD bisects <ABC so that 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  16. Pairs Of Angles : Types • Adjacent angles • Vertically opposite angles • Complimentary angles • Supplementary angles • Linear pairs of angles 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  17. 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. 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  18. 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. 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  19. 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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  20. 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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  21. 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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  22. 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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  23. 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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  24. 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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  25. 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 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  26. How to measure an angle using a protractor • http://www.youtube.com/watch?v=FeclDm7pVcI&feature=related 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

  27. How to draw an angle using a protractor • http://www.youtube.com/watch?v=X3IO6Uhtlp8&feature=related 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

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