1. 8-3 Do Now Draw each figure. 1. line segment 2. line 3. ray 4. plane
Course 2
8-3
EQ: How do I identify parallel, perpendicular, and angles
formed by a transversal?
Do Now
Draw each figure.
1. line segment
2. line
3. ray
4. plane
HWK: Wbk P 70

2. M7A2a Given a problem, define a variable, write an equation, solve the equation and interpret the solution.

3. Insert Lesson Title Here
Course 2
Angles
Insert Lesson Title Here
Vocabulary Review
Angle –
Vertex -
right angle - angle that that measures. The symbol Γ indicates a right angle.

4. acute angle - is an angle that measures
obtuse angle - an angle that measures
straight angle - is an angle that measures
complementary angles – the sum of the measures of two angles is ?0
supplementary angles – the sum of the measures of two angles is ?°

5. New Vocabulary

6. perpendicular lines - angles formed by two intersecting lines are equal to 90°
parallel lines - lines in the same plane do not intersect at all
adjacent angles – angles that have a common vertex and a common side, but no common interior points.

7. vertical angles - opposite angles formed by two intersecting lines
Transversal - a line that intersects two or more lines
corresponding angles - are angles on the same side of the transversal and are both above or both below the parallel lines

8. Course 2
8-3
Angles A C B 1
Vertex
An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex.
Angles are measured in degrees (°).

9. 8-3 Angles An angle’s measure determines the type of angle it is.
Course 2
8-3
Angles
An angle’s measure determines the type of
angle it is.
A right angle is an angle that
that measures exactly 90°. The
symbol indicates a right angle.
An acute angle is an angle
that measures less than 90°.
An obtuse angle is an angle
that measures more than 90°
but less than180°.
A straight angle is an angle
that measures 180°.

10. Additional Example 1: Classifying Angles
Course 2
8-3
Angles
Additional Example 1: Classifying Angles
Tell whether each angle is acute, right, obtuse or straight. A. B.
obtuse angle
acute angle

11. Insert Lesson Title Here
Course 2
8-3
Angles
Insert Lesson Title Here
Check It Out: Example 1
Tell whether each angle is acute, right, obtuse, or straight. B. A.
straight angle
acute angle

12. 8-3 Angles Reading Math You can name this angle ABC, CBA, B, or 1.
Course 2
8-3
Angles
You can name this angle ABC, CBA, B, or 1.
Reading Math
A •
B •
• C 1

13. 8-3 Angles If the sum of the measures of two angles is
Course 2
8-3
Angles
If the sum of the measures of two angles is
90°, then the angles are complementary
angles. If the sum of the measures of two
angles is 180°, then the angles are
supplementary angles.

14. Course 2
8-3
Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
OMP and PMQ O N P Q R M
complementary.

15. Course 2
8-3
Angles
If the angle you are measuring appears obtuse, then it measure is greater than 90°. If the angle is acute, its measure is less than 90°.
Reading Math

16. Course 2
8-3
Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither. O N P Q R M
NMO and OMR

17. Course 2
8-3
Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither. O N P Q R M
PMQ and QMR

18. Course 2
8-3
Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
BAC and CAF C B D E F A

19. Course 2
8-3
Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither. C B D E F A
CAD and EAF

20. Course 2
8-3
Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither. C B D E F A
BAC and EAF

21. Course 2
8-3
Angles
Angles A and B are complementary. If mA is 56°, what is the mB? What is the supplement of A?

22. Course 2
8-3
Angles
Angles P and Q are supplementary. If mP is 32°, what is the mQ? What is the complement of P?

23. Course 2
8-3
Angle Relationships
The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Reading Math

24. Course 2
8-3
Angle Relationships
Tell whether the lines appear parallel or perpendicular.
UV and YV
The lines appear to intersect to form right angles.
UV  YV

25. Course 2
8-3
Angle Relationships
Tell whether the lines appear parallel or perpendicular.
XY and WZ
The lines are in the same plane and do not intersect.
XY || WZ

26. Course 2
8-3
Angle Relationships
Tell whether the lines appear parallel or perpendicular.
WX and XU
WX  XU
The lines appear to intersect to form right angles.

27. Course 2
8-3
Angle Relationships
Tell whether the lines appear parallel or perpendicular.
WX and ZY
The lines are in the same plane and do not intersect.
WX || ZY

28. Course 2
8-3
Angle Relationships
Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary

29. Vertical angles are the opposite angles formed by two intersecting lines. When two lines intersect, two pairs of vertical angles are formed. Vertical angles have the same measure, so they are congruent.

30. Course 2
8-3
Angle Relationships
Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

31. Course 2
8-3
Angle Relationships
A transversal is a line that intersects two or more lines. Line t is a transversal. When the lines that are intersected are parallel, four pairs of corresponding angles are formed.

32. Corresponding angles are on the same side of the transversal and are both above or both below the parallel lines. Angles 1 and 5 are corresponding angles. Corresponding angles are congruent.

33. 8-3 Angle Relationships Line n line p. Find the measure of the angles.
Course 2
8-3
Angle Relationships
Line n line p. Find the measure of the angles.

34. 8-3 Angle Relationships 45° 4 5 6 2 3 7 n p
Course 2
8-3
Angle Relationships
Line n line p. Find the measure of the angles.
45° 4 5 6 2 3
135° 7 n p

35. Insert Lesson Title Here
Course 2
8-3
Angles TOTD
Insert Lesson Title Here
Tell whether each angle is acute, right, obtuse, or straight. 1.
straight 2.
obtuse

36. Insert Lesson Title Here
Course 2
8-3
Angles TOTD
Insert Lesson Title Here
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
3. AZB and BZC
neither
4. BZC and CZD
complementary
5. Angles M and N are supplementary. If M is 117°, what is mN?
63°

37. Angle Relationships TOTD Insert Lesson Title Here
Course 2
8-3
Angle Relationships TOTD
Insert Lesson Title Here
Tell whether the lines appear
parallel, perpendicular, or skew.
1. AB and CD
2. EF and FH
parallel
perpendicular