1. Points, Lines, Planes, and Angles
7-1
Points, Lines, Planes, and Angles
Warm Up
Problem of the Day
Lesson Presentation
Course 3

2. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Warm Up
Solve.
1. x + 30 = 90
x = 180
x = 180
4. 90 = 61 + x
5. x + 20 = 90
x = 60
x = 77
x = 148
x = 29
x = 70

3. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Problem of the Day
Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, of the class wants sausage on the pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza? 1 3 1 6

4. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Learn to classify and name figures.

5. Insert Lesson Title Here
Course 3
7-1
Points, Lines, Planes, and Angles
Insert Lesson Title Here
Vocabulary
point line plane
segment ray angle
right angle acute angle
obtuse angle complementary angles
supplementary angles
vertical angles
congruent

6. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.

7. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
A point names a location.
• A
Point A

8. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
A line is perfectly straight and extends forever in both directions. B C l
line l, or BC

9. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
A plane is a perfectly flat surface that extends forever in all directions. P E
plane P, or plane DEF D F

10. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
A segment, or line segment, is the part of a line between two points. H GH G

11. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
A ray is a part of a line that starts at one point and extends forever in one direction. J KJ K

12. Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
A. Name 4 points in the figure.
Point J, point K, point L, and point M
B. Name a line in the figure.
KL or JK
Any 2 points on a line can be used.

13. Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
C. Name a plane in the figure.
Plane , plane JKL
Any 3 points in the plane that form a triangle can be used.

14. Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
D. Name four segments in the figure.
JK, KL, LM, JM
E. Name four rays in the figure.
KJ, KL, JK, LK

15. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 1
A. Name 4 points in the figure.
Point A, point B, point C, and point D
B. Name a line in the figure.
DA or BC
Any 2 points on a line can be used. A B C D

16. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 1
C. Name a plane in the figure.
Plane , plane ABC, plane BCD, plane CDA, or plane DAB
Any 3 points in the plane that form a triangle can be used. A B C D

17. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 1
D. Name four segments in the figure
AB, BC, CD, DA
E. Name four rays in the figure
DA, AD, BC, CB A B C D

18. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
An angle () is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees.
One degree, or 1°, is of a circle. m1
means the measure of 1. The angle can be named XYZ, ZYX, 1, or Y. The vertex must be the middle letter. 1
360 X Y Z 1
m1 = 50°

19. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°. F K J G H

20. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
The measures of angles that fit together to form a complete circle, such as MRN, NRP, PRQ, and QRM, add to 360°. P R Q M N

21. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
A right angle measures 90°.
An acute angle measures less than 90°.
An obtuse angle measures greater than 90° and less than 180°.
Complementary angles have measures that add to 90°.
Supplementary angles have measures that add to 180°.

22. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
A right angle can be labeled with a small box at the vertex.
Reading Math

23. Additional Example 2: Classifying Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
A. Name a right angle in the figure.
TQS
B. Name two acute angles in the figure.
TQP, RQS

24. Additional Example 2: Classifying Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
C. Name two obtuse angles in the figure.
SQP, RQT

25. Additional Example 2: Classifying Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
D. Name a pair of complementary angles.
TQP, RQS
mTQP + m RQS = 47° + 43° = 90°

26. Additional Example 2: Classifying Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
E. Name two pairs of supplementary angles.
TQP, RQT
mTQP + m RQT = 47° + 133° = 180°
SQP, SQR
mSQP + m SQR = 137° + 43° = 180°

27. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 2
A. Name a right angle in the figure.
BEC E D C B A
90°
75°
15°

28. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 2
B. Name two acute angles in the figure.
AEB, CED
C. Name two obtuse angles in the figure.
BED, AEC E D C B A
90°
75°
15°

29. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 2
D. Name a pair of complementary angles.
AEB, CED
mAEB + m CED = 15° + 75° = 90° E D C B A
90°
75°
15°

30. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 2
E. Name two pairs of supplementary angles.
AEB, BED
mAEB + mBED = 15° + 165° = 180°
CED, AEC
mCED + mAEC = 75° + 105° = 180° E D C B A
90°
75°
15°

31. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Congruent figures have the same size and shape.
Segments that have the same length are congruent.
Angles that have the same measure are congruent.
The symbol for congruence is , which is read “is congruent to.”
Intersecting lines form two pairs of vertical angles. Vertical angles are always congruent, as shown in the next example.

32. Additional Example 3A: Finding the Measure of Vertical Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 3A: Finding the Measure of Vertical Angles
In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.
If m1 = 37°, find m 3.
The measures of 1 and 2 are supplementary.
m2 = 180° – 37° = 143°
The measures of 2 and 3 are supplementary.
m3 = 180° – 143° = 37°
So m1 = m3 or m1 = m3. ~

33. Additional Example 3B: Finding the Measure of Vertical Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Additional Example 3B: Finding the Measure of Vertical Angles
In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.
If m4 = y°, find m2.
m3 = 180° – y°
m2 = 180° – (180° – y°)
= 180° – 180° + y°
Distributive Property m2 = m4
= y°
So m4 = m2 or m4  m2.

34. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 3A
In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 2 3
If m1 = 42°, find m3. 1 4
The measures of 1 and 2 are supplementary.
m2 = 180° – 42° = 138°
The measures of 2 and 3 are supplementary.
m3 = 180° – 138° = 42°
So m1 = m3 or m1  m3.

35. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Check It Out: Example 3B
In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 2 3
If m4 = x°, find m2. 1 4
m3 = 180° – x°
m2 = 180° – (180° – x°)
= 180° –180° + x°
Distributive Property m2 = m4
= x°
So m4 = m2 or m4  m2.

36. Points, Lines, Planes, and Angles
Course 3
7-1
Points, Lines, Planes, and Angles
Lesson Quiz
In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.
1. Name three points in the figure.
Possible answer: A, B, and C
2. Name two lines in the figure.
Possible answer: AD and BE
3. Name a right angle in the figure.
Possible answer: AGF
4. Name a pair of complementary angles.
Possible answer: 1 and 2
5. If m1 = 47°, then find m 3.
47°