Geometry Do Now: Name each figure 1) 2) 3) Draw a line AD with a midpoint C, then write all congruent segment using correct notation. Take out: Binder, Pencil, Do Now Sheet, Homework 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Vertically Opposite Angles Vertically opposite angles are pairs of angles formed by two lines intersecting at a point. A D B C ÐAPC = ÐBPD P ÐAPB = ÐCPD Four angles are formed at the point of intersection. Vertically opposite angles are congruent. Point of intersection ‘P’ is the common vertex of the four angles. 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

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 600 + 300 = 900 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

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 700 + 300 = 1000 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

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 1000 + 800 = 1800 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

ÐDEF and ÐPQR are not supplementary because Contd…. If the sum of two angles is more than 1800 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 1100 + 800 = 1900 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

Two adjacent supplementary angles are called linear pair of angles. 1200 600 C D P ÐAPC + ÐAPD 600 + 1200 = 1800 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

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

Adjacent angles: ÐAPC and ÐCPD Name the vertically opposite angles and adjacent angles in the given figure: A D B C P 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

How to measure an angle using a protractor http://www.youtube.com/watch?v=FeclD m7pVcI&feature=related 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

How to draw an angle using a protractor http://www.youtube.com/watch?v=X3IO6 Uhtlp8&feature=related 9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors