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1-3 Warm Up Lesson Presentation Lesson Quiz Holt Geometry Measuring and Constructing Angles * * * * * * * * * * * * * Welcome Geometric Thinkers! 1. – PowerPoint PPT presentation

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Title: Measuring and


1
Measuring and Constructing Angles
1-3
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry
2
Welcome Geometric Thinkers!
  • 1. Draw AB and AC, where A, B, and C are
    noncollinear.
  • 2. Draw opposite rays DE and DF.
  • Solve each equation.
  • 3. 2x 3 x 4 3x 5 180

3
Objectives
Name and classify angles. Measure and construct
angles and angle bisectors.
4
Vocabulary
angle right angle vertex obtuse
angle interior of an angle straight
angle exterior of an angle congruent
angles measure angle bisector degree acute
angle
5
An angle is a figure formed by two rays, or
sides, with a common endpoint called the vertex
(plural vertices). You can name an angle several
ways by its vertex, by a point on each ray and
the vertex, or by a number.
6
The set of all points between the sides of the
angle is the interior of an angle. The exterior
of an angle is the set of all points outside the
angle.
Angle Name ?R, ?SRT, ?TRS, or ?1
You cannot name an angle just by its vertex if
the point is the vertex of more than one angle.
In this case, you must use all three points to
name the angle, and the middle point is always
the vertex.
7
Example 1 Naming Angles
A surveyor recorded the angles formed by a
transit (point A) and three distant points, B, C,
and D. Name three of the angles.
Possible answer
?BAC
?CAD
?BAD
8
Check It Out! Example 1
Write the different ways you can name the angles
in the diagram.
?RTQ, ?T, ?STR, ?1, ?2
9
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10
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11
Song Alert Types of Angles (tune of YMCA)
12
Angles YMCA http//www.youtube.com/watch?vrCCQLX0
Fh_M
  • Angles we learn all about
  • Angles there are different types of
  • Angles we classify them they are
  • Right, Straight, Obtuse, Acute
  • Repeat!!!
  • Types of angles are
  • Right straight obtuse (types of angles are )
  • Right straight acute (types of angles are )
  • A right angle is 90 degrees and a straight one is
    180
  • Right straight obtuse (types of angles are )
  • Right straight acute (types of angles are )
  • Obtuse is more than 90 degrees and acute is less
    than 90

13
Check It Out! Example 2
Use the diagram to find the measure of each
angle. Then classify each as acute, right, or
obtuse.
a. ?BOA b. ?DOB c. ?EOC
m?BOA 40
?BOA is acute.
m?DOB 125
?DOB is obtuse.
m?EOC 105
?EOC is obtuse.
14
Congruent angles are angles that have the same
measure. In the diagram, m?ABC m?DEF, so you
can write ?ABC ? ?DEF. This is read as angle
ABC is congruent to angle DEF. Arc marks are
used to show that the two angles are congruent.
The Angle Addition Postulate is very similar to
the Segment Addition Postulate that you learned
in the previous lesson.
15
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16
Example 3 Using the Angle Addition Postulate
m?DEG 115, and m?DEF 48. Find m?FEG
m?DEG m?DEF m?FEG
? Add. Post.
115? 48? m?FEG
Substitute the given values.
Subtract 48 from both sides.
67? m?FEG
Simplify.
17
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18
Example 4 Finding the Measure of an Angle
19
Check It Out! Example 4b
Find the measure of each angle.
Step 1 Find x.
?LJK ?KJM
Def. of ? bisector
(10x 3) (x 21)
Substitute the given values.
Add x to both sides.
Simplify.
9x 3 21
Subtract 3 from both sides.
9x 18
Divide both sides by 9.
x 2
Simplify.
20
Practice
  • P.25 12-22, 27, 29-34, 37, 38, 41-43, 53, 56

21
Lesson Quiz Part I
Classify each angle as acute, right, or obtuse.
1. ?XTS
acute
right
2. ?WTU
3. K is in the interior of ?LMN, m?LMK 52, and
m?KMN 12. Find m?LMN.
64
22
Lesson Quiz Part II
32
5. Use a protractor to draw an angle with a
measure of 165.
23
Lesson Quiz Part III
6. m?WYZ (2x 5) and m?XYW (3x 10). Find
the value of x.
35
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