LINE, Point and PLANE

1. 5-1 Points, Lines, Planes, and Angles
5-1 Points, Lines, Planes, and Angles
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra

2. 5-1 Points, Lines, Planes, and Angles
Warm Up
Solve.
1. x + 30 = 90 x = 60
2. 103 + x = 180 x = 77
3. 32 + x = 180 x = 148
4. 90 = 61 + x x = 29
5. x + 20 = 90 x = 70
Pre-Algebra

3. 5-1 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, 1 of the class wants sausage on the
3
pizza, and the rest want only cheese on
the pizza. What fraction of Mrs. Meyer’s
class wants just cheese on the pizza?
1
6
Pre-Algebra

4. 5-1 Points, Lines, Planes, and Angles
Learn to classify and name figures.
Pre-Algebra

5. 5-1 Points, Lines, Planes, and Angles
Vocabulary
point line plane
segment ray angle
right angle acute angle
obtuse angle complementary angles
supplementary angles
vertical angles
congruent
Pre-Algebra

6. 5-1 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.
Pre-Algebra

7. 5-1 Points, Lines, Planes, and Angles
A point names a •A Point A
location.
Pre-Algebra

8. 5-1 Points, Lines, Planes, and Angles
A line is perfectly
C
straight and l
extends forever in B line l, or BC
both directions.
Pre-Algebra

9. 5-1 Points, Lines, Planes, and Angles
A plane is a
perfectly flat P E
surface that D plane P, or
F plane DEF
extends forever in
all directions.
Pre-Algebra

10. 5-1 Points, Lines, Planes, and Angles
A segment, or H
line segment, is
the part of a line GH
between two G
points.
Pre-Algebra

11. 5-1 Points, Lines, Planes, and Angles
A ray is a part of
J
a line that starts
at one point and KJ
extends forever in K
one direction.
Pre-Algebra

12. 5-1 Points, Lines, Planes, and Angles
Additional Example 1A & 1B: 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.
Pre-Algebra

13. 5-1 Points, Lines, Planes, and Angles
Additional Example 1C: 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.
Pre-Algebra

14. 5-1 Points, Lines, Planes, and Angles
Additional Example 1D & 1E: 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
Pre-Algebra

15. 5-1 Points, Lines, Planes, and Angles
Try This: Example 1A & 1B
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
D C
Pre-Algebra

16. 5-1 Points, Lines, Planes, and Angles
Try This: Example 1C
C. Name a plane in the figure.
Plane , plane ABC, Any 3 points in the
plane BCD, plane CDA, plane that form a
or plane DAB triangle can be used.
A B
D C
Pre-Algebra

17. 5-1 Points, Lines, Planes, and Angles
Try This: Example 1D & 1E
D. Name four segments in the figure
AB, BC, CD, DA
E. Name four rays in the figure
DA, AD, BC, CB
A B
D C
Pre-Algebra

18. 5-1 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.
1
One degree, or 1°, is of a circle. m∠1
360
means the measure of ∠1. The angle can be
named ∠XYZ, ∠ZYX, ∠1, or ∠Y. The vertex must
be the middle letter.
X
1 m∠1 = 50°
Y Z
Pre-Algebra

19. 5-1 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°.
G H
F K J
Pre-Algebra

20. 5-1 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
N
R Q
M
Pre-Algebra

21. 5-1 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°.
Pre-Algebra

22. 5-1 Points, Lines, Planes, and Angles
Reading Math
A right angle can be labeled with a small box at
the vertex.
Pre-Algebra

23. 5-1 Points, Lines, Planes, and Angles
Additional Example 2A & 2B: Classifying Angles
A. Name a right angle in the figure.
∠TQS
B. Name two acute angles in the figure.
∠TQP, ∠RQS
Pre-Algebra

24. 5-1 Points, Lines, Planes, and Angles
Additional Example 2C: Classifying Angles
C. Name two obtuse angles in the figure.
∠SQP, ∠RQT
Pre-Algebra

25. 5-1 Points, Lines, Planes, and Angles
Additional Example 2D: Classifying Angles
D. Name a pair of complementary angles.
∠TQP, ∠RQS m∠TQP + m∠ RQS = 47° + 43° = 90°
Pre-Algebra

26. 5-1 Points, Lines, Planes, and Angles
Additional Example 2E: Classifying Angles
E. Name two pairs of supplementary angles.
∠TQP, ∠RQT m∠TQP + m∠RQT = 47° + 133° = 180°
∠SQP, ∠RQS m∠SQP + m∠RQS = 137° + 43° = 180°
Pre-Algebra

27. 5-1 Points, Lines, Planes, and Angles
Try This: Example 2A
A. Name a right angle in the figure.
∠BEC
C
B
A 90° D
15° 75°
E
Pre-Algebra

28. 5-1 Points, Lines, Planes, and Angles
Try This: Example 2B & 2C
B. Name two acute angles in the figure.
∠AEB, ∠CED
C. Name two obtuse angles in the figure.
∠BED, ∠AEC
C
B
A 90° D
15° 75°
E
Pre-Algebra

29. 5-1 Points, Lines, Planes, and Angles
Try This: Example 2D
D. Name a pair of complementary angles.
∠AEB, ∠CED m∠AEB + m∠CED = 15° + 75° = 90°
C
B
A 90° D
15° 75°
E
Pre-Algebra

30. 5-1 Points, Lines, Planes, and Angles
Try This: Example 2D & 2E
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°
C
B
A 90° D
15° 75°
E
Pre-Algebra

31. 5-1 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.
Pre-Algebra

32. 5-1 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.
A. If m∠1 = 37°, find m∠ 3.
The measures of ∠1 and ∠2 add to 180° because they
are supplementary, so m∠2 = 180° – 37° = 143°.
The measures of ∠2 and ∠3 add to 180° because they
are supplementary, so m∠3 = 180° – 143° = 37°.
Pre-Algebra

33. 5-1 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.
B. If m∠4 = y°, find m∠2.
m∠3 = 180° – y°
m∠2 = 180° – (180° – y°)
= 180° – 180° + y° Distributive Property
= y° m∠2 = m∠4
Pre-Algebra

34. 5-1 Points, Lines, Planes, and Angles
Try This: Example 3A
In the figure, ∠1 and ∠3 are vertical
angles, and ∠2 and ∠4 are vertical angles.
2
A. If m∠1 = 42°, find m∠3. 3
1
4
The measures of ∠1 and ∠2 add to 180° because they
are supplementary, so m∠2 = 180° – 42° = 138°.
The measures of ∠2 and ∠3 add to 180° because they
are supplementary, so m∠3 = 180° – 138° = 42°.
Pre-Algebra

35. 5-1 Points, Lines, Planes, and Angles
Try This: Example 3B
In the figure, ∠1 and ∠3 are vertical
angles, and ∠2 and ∠4 are vertical
angles.
2
B. If m∠4 = x°, find m∠2. 3
1
4
m∠3 = 180° – x°
m∠2 = 180° – (180° – x°)
= 180° –180° + x° Distributive Property
= x° m∠2 = m∠4
Pre-Algebra

36. 5-1 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°
Pre-Algebra