8.1 angles 1

1. Daily Homework Quiz For use after Lesson 7.3
Use a percent proportion to answer the question.
1.28 is what percent of 80?2.15 is 5% of what number?

2. Daily Homework Quiz For use after Lesson 7.3
Use a percent proportion to answer the question.
ANSWER 35%
1.28 is what percent of 80?2.15 is 5% of what number?
ANSWER 300

3. Chapter 8.1
Lines and Angles

4. Essential Questions
•Why is it important to be able to identify
congruent triangles in everyday life?
•Where in real life can you use the
properties of isosceles and equilateral
triangles?
•How are the relationships between lines
and planes used in the real world?
•What areas in the real world are properties
of parallel lines important?

5. Chapter 8 Section 1
•Vocabulary 1-14

6. Prerequisite Skills VOCABULARY CHECK
APoint: a figure without dimensions.
Line: a figure that extends without end in two
opposite directions.
X Y XY
Ray: a figure that has one endpoint and
extends without end in one direction.
C D
CD

7. •Plane : A flat surface that extends without
end.
•Angle: a figure formed by two rays that begin
at a common point called the vertex.
C
A
B
Vertex
Vertex: end point of the rays that form an angle.

8. •Degree: unit of measure. 95
0

9. Prerequisite Skills VOCABULARY CHECK
Identify the object with the review word from the
list: point, line, ray, plane, angle, vertex, degree.
2.
1.
3.
ANSWER line
ANSWER point
ANSWER ray
4. A unit for measuring angles is a(n) ? .
ANSWER degree

10. Classifying Angles
•Angles are classified by degrees.
•Acute - greater than 0 degrees but less than
90 degrees.
C
A
B
This is read “Angle ABC or
Angle CBA, or just Angle B
ABCÐ

11. Classifying Angles
•Obtuse – angles measuring more than 90
degrees but less than 180 degrees.

12. Classifying Angles
•Right Angles measure exactly 90
degrees and labeled with “square” in the
corner of the angle.

13. Classifying Angles
•A straight angle “looks like” a straight line,
but it actually is an angle. It measures
exactly 180 degrees.
A B C
180ABC mÐ = °

14. Two angles are complementary if the sum of
their measures is 90 degrees.
70 °
20 °
70 + 20 = 90 degrees.

15. •Are these complementary angles?
60 °
30 °

16. •Two angles are supplementary if the sum of
their measures is 180 degrees.
1 2 180m mÐ + Ð = °
1 2

17. GUIDED PRACTICE for Example 1
Tell whether 1 and 2 are complementary,
supplementary, or neither.
1.m 1 = 79
m 2 = 101
SOLUTION
m 1+ m 2
=79° + 101°
ANSWER
Hence, the angles are supplementary.
=180

18. GUIDED PRACTICE for Example 1
Tell whether 1 and 2 are complementary,
supplementary, or neither.
2.m 1 = 64
m 1 = 36
SOLUTION
m 1+ m 2
=100°
=64 + 36
ANSWER
Hence, 1 and 2 are neither complementary nor
supplementary.

19. GUIDED PRACTICE for Example 1
Tell whether 1 and 2 are complementary,
supplementary, or neither.
3.m 1 = 52
m 1 = 38
SOLUTION
m 1+ m 2
=52 + 38
=90
ANSWER
Hence, 1 and 2 are complementary.

20. Vertical Angles
When two lines intersect at a point, they
form two pairs of vertical angles. They do
not share a side, and they have the same
measure.
1
3
4
2
Angles 1 & 2 are vertical angles and 3&4 are vertical
angles.

21. GUIDED PRACTICE for Example 2
Find the measures of the numbered angles.
SOLUTION
It is given that m 5 = 137 .
STEP 1
5 and 7 are vertical angles.Their measures
are equal, so m 7= 137 ° .
137°
43°
43°

22. GUIDED PRACTICE for Example 2
Find the measures of the numbered angles.
SOLUTION
It is given that m 8 = 54 .
STEP 1
8 and 10 are vertical angles. Their measures
are equal, so m 10= 54 ° .
54°
126°
126°

23. Homework
•Page 406 #1-11