Angle Measure

1
Lesson 1-4

• Angle Measure

2
Lesson Outline

• Five-Minute Check
• Then Now and Objectives
• Vocabulary
• Key Concept
• Examples
• Lesson Checkpoints
• Summary and Homework

3
Then and Now
You measure line segments (Lesson 12)

• Measure and classify angles
• Identify and use congruent angles an the bisector
  of an angle

4
Objectives

• Measure and classify angles
• Obtuse m? gt 90
• Right m? 90 (the corner of a piece of
  paper)
• Acute m? lt 90
• Identify and use congruent angles an the bisector
  of an angle

5
Vocabulary

• Degree one three hundred and sixtieth of a
  circle
• Ray part of a line with one end point
• Opposite rays are collinear rays with the same
  end point ( form a 180 degree angle)
• Angle is formed by 2 noncollinear rays with a
  common endpoint (vertex)
• Sides composed of rays
• Vertex is the common endpoint
• Interior area between the two rays that form
  the angle
• Exterior area not between the two rays that
  form the angle

6
Vocabulary (cont)

• Special types of angles
• Right angle measure equals 90 degrees
• Acute angle measure is less than 90 degrees
• Obtuse angle measure is greater than 90 degrees
  (but less than 180)
• Angle Bisector a ray that divides an angle into
  two congruent angles

7
Example 1
Name all angles that have B as a vertex.
Answer ?5, ?6, ?7, and ?ABG
Name the sides of ?5.
Write another name for ?6.
Answer ?EBD, ?FBD, ?DBF, and ?DBE are other
names for ?6.
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Key Concept

• An easy measuring device is the corner of a piece
  of notebook paper (or computer paper). It is a
  right angle.

9
Example 2a
Measure ?TYV and classify it as right, acute,
or obtuse.
?TYV is marked with a right angle symbol, so
measuring is not necessary.
10
Example 2b
Measure ?WYT and classify it as right, acute, or
obtuse.
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Example 2c
Measure ?TYU and classify it as right, acute, or
obtuse.
Use a protractor to find that m ?TYU 45 .
Answer Since 45 lt 90, then ?TYU is an acute
angle.
12
Example 3
INTERIOR DESIGN Wall stickers of standard shapes
are often used to provide a stimulating
environment for a young childs room. A
five-pointed star sticker is shown with vertices
labeled. Find m?GBH and m?HCI if ?GBH ? ?HCI,
m?GBH 2x 5, and m?HCI 3x 10.
Step 1 Solve for x.
?GBH ? ?HCI Given
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Example 3 cont
m?GBH m?HCI Definition of congruent angles 2x
5 3x 10 Substitution 2x 15 3x Add 10
to each side. 15 x Subtract 2x from each side.
Step 2 Use the value of x to find the measure of
either angle.
m?GBH 2x 5 Given 2(15)
5 Substitution, x 15 30 5 35 Simplify.
Answer m?GBH 35, m?HCI 35
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Lesson Checkpoints
15
Summary Homework

• Summary
• Angles are named by 3 points with the vertex in
  the middle (or by vertex letter if no confusion)
• Angles are classified as acute, right, or obtuse
  according to their measure
• An angle bisector is a ray that divides an angle
  into two congruent angles (halves)
• Ray is equidistance from the sides of the angle
• Homework
• pg 41-3 30-35, 39-42