1. 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 #’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. 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

4. 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

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. 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

7. 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

8. 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

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.
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. 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

15. 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

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. 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

18. 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

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

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

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

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

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

24. 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

25. 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

26. How to measure an angle using a protractor
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9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors

27. How to draw an angle using a protractor
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9/7/2010 Objective: Name, draw, label, and measure angles, and determine angle bisectors