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1-4: Measuring Angles

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1-4: Measuring Angles Parts of an Angle An angle is formed by two rays with the same endpoint. The rays are the sides of the angle and the endpoint is the ... – PowerPoint PPT presentation

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Title: 1-4: Measuring Angles


1
1-4 Measuring Angles
2
Parts of an Angle
  • An angle is formed by two rays with
    the same endpoint.
  • The rays are the sides of the angle and the
    endpoint is the vertex of the angle.
  • The interior of an angle is the
    region containing all points
    between the sides of the angle.
  • The exterior of an angle is the region containing
    all points outside the angle.

3
Naming an Angle
  • You can name an angle by its vertex (?A), a point
    on each ray and the vertex (?BAC or ?CAB), or a
    number (?1).
  • Note When using 3 points to name an angle, the
    vertex must go in the middle!

4
Naming Angles
  • What are two other names for ?1?
  • What are two other names for ?KML?

5
Measuring Angles
  • One way to measure the size of
    an angle is in degrees.
  • To say that the measure of ?A
    is 62?, you would write m?A 62?.
  • Protractor Postulate Consider OB and point A on
    one side of OB. Every ray of the form OA can be
    paired one to one
    with a real
    number
    from 0 to 180.

6
Types of Angles
  • You can classify angles according to their
    measures.

Symbol for right angle!
7
Measuring and Classifying Angles
  • What are the measures of ?LKN, ?JKL, and ?JKN?
  • Classify each as acute, right, obtuse, or
    straight.

8
Congruent Angles
  • Angles with the same measure are congruent
    angles.
  • This means that if m?A m?B, then
    ?A ? ?B (and vice versa).
  • You can mark angles with arcs to show they are
    congruent.

9
Using Congruent Angles
  • Synchronized swimmers form angles with their
    bodies.
  • If m?GHJ 90?,
    what is m?KLM?
  • If m?ABC 49?,
    what is m?DEF?

10
? Which angle is congruent to ?WBM?
11
Angle Addition
  • Angle Addition Postulate If point B is in the
    interior of ?AOC, then
    m?AOB m?BOC m?AOC.

12
Using the Angle Addition Postulate
  • If m?RQT 155?, what are m?RQS and m?TQS?

13
? If m?ABC 175?, what are m?ABD and m?CBD?
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