Download L5 - Angle Measures

Chapter 1, Lesson 5
Objective:
Date:
Students will learn to measure and classify angles, and use congruent angles and the bisector
of an angle.
Wups
1. Use the number line to find each measure.
a. AC
b. DE
2. Find the distance between P(-2, 5) and Q(4, -3)
A. Vocabulary
Term
Definition
Example
Ray
Part of a line. It has one endpoint and
extends indefinitely in one direction.
Angle
Formed by two noncollinear rays that
have a common endpoint.
Vertex
The common endpoint of an angle.
Congruent
Angles
Angles that have the same measure.
Angle Bisector
A ray that divides an angle into two
congruent angels.
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Types of Angles
Angle Type
Measure
Example
Right Angle
m∠A = 90˚
Acute Angle
m∠A < 90˚
Obtuse Angle
90˚ < m∠A < 180˚
Straight Angle
mA = 180
B. Examples: Classify each angle as acute, obtuse, right, or straight.
1.
2.
3.
4.
5. 89
6. 21
7. 180
8. 90
C. Naming Angles
Three ways to name an angle:
1. One Point
A
P
B
2. Three Point Name
A
E : Which angle does this name???
B
E
D
C
2
A
Example: Name all the angles in the figure.
C
B
D
3. Number Inside the Angle
4
1
3
2
D. Examples
9. Refer to the diagram at the right.
a. Name all angles that have B as a vertex.
b. Name the sides of ∠5.
c. Write another name for ∠6.
10. Classify each angle as right, acute, or obtuse.
a. ∠MPR
b. ∠RPN
c. ∠NPS
⃗⃗⃗⃗⃗ are opposite rays.
11. ⃗⃗⃗⃗⃗
𝑄𝑆 bisects ∠PQT, and ⃗⃗⃗⃗⃗
𝑄𝑃 and 𝑄𝑅
a. If m∠PQT = 60 and m∠PQS = 4x + 14, find the value of x
b. If m∠PQS = 3x + 13 and m∠SQT = 6x – 2, find m∠PQT.
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12. ⃗⃗⃗⃗⃗
𝐵𝐴 and⃗⃗⃗⃗⃗⃗
𝐵𝐶 are opposite rays, ⃗⃗⃗⃗⃗
𝐵𝐹 bisects ∠CBE, and⃗⃗⃗⃗⃗⃗⃗
𝐵𝐷 bisects ∠ABE.
a. If m∠EBF = 6x + 4 and m∠CBF = 7x – 2, find m∠EBC.
b. If m∠1 = 4x + 10 and m∠2 = 5x, find m∠2.
c. If m∠2 = 6y + 2 and m∠1 = 8y – 14, find m∠ABE.
E. Summary
Match each description in the first column with one of the terms in the second column.
1. angle that measures between 0 and 90
a. acute angle
2. angle that measures between 90 and 180
b. vertex
3. a ray that divides an angle into two congruent angles
c. straight angle
4. angle that measures exactly 90
d. angle bisector
5. a line segment (degree measure of 180)
e. obtuse angle
6. where two segments or rays meet to form an angle
f. right angle
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