1. Line and Angle Relationships

2. .A or Point A Points, Lines, and Rays
Sometimes it’s necessary to refer to a specific point in space
Points have no size
The only function of a point is to show position
.A or Point A

3. Points, Lines, and Rays
If you draw two points on a sheet of paper, a line can be used to connect them
Lines need names just like points do, so we can refer to them easily
Line segment AB or
Line AB or AB

4. Points, Lines, and Rays
Since the length of any line is infinite, we sometimes use parts of a line
A ray is the part of a line that extends without end in one direction
In “ray AB,” ( ) A is the endpoint
The second point that is used to name the ray can be any point other than the endpoint (You could also name it ray AC)

5. Points, Lines, and Rays
A plane is a set of line segments or sides that connect to form a closed figure
Plane ABCD A B
D C

6. Points, Lines, and Rays Checkpoint
Look at the line below:
Name a line segment
Name a ray in two different ways
What is the endpoint of ray BC?
Line segments AB, AC, BA, BC, CB, and CA
Ray AB and Ray AC, or Ray CB and Ray CA B

7. Naming Angles Two different rays with the same endpoint form an angle
The point they have in common is called the vertex of the angle
The rays form the sides of the angle

8. Naming Angles The angle above is made up of ray BA and ray BC
B is the common endpoint
Point B is the vertex of the angle
Instead of using the word angle, you can use the symbol for angle, which is

9. Naming Angles There are several ways to name an angle
Using the three letters of the points that make up the two rays with the vertex as the middle letter ( ABC, or CBA)
Use just the letter of the vertex ( B)

10. Naming Angles
When more than one angle is formed by a vertex, you use three letters to name each angle
Since A is the vertex of 3 different angles, each angle needs three letters to name it ( CAD, CAB, and BAD)

11. Naming Angles Checkpoint
Look at the angles formed by the rays below:
Name the vertex
Name all three of the angles Y
Angles XYZ, XYW, and WYZ

12. Measuring Angles You measure an angle in degrees using a protractor
Place the center point of the protractor on the vertex of the angle
Align the 0 degrees line on the protractor with one side of the angle
Read the number of degrees on the scale where it intersects the second side of the angle

13. Measuring Angles Checkpoint
Measure each angle
Answers should be close to 60, 30, and 20 degrees. On my projector, the line covers about 10 degrees

14. Classifying Angles An acute angle measures less than 90 degrees
A right angle measures exactly 90 degrees

15. Classifying Angles An obtuse angle measures greater than 90 degrees
A straight angle measures exactly 180 degrees

16. Classifying Angles
A reflex angle measures greater than 180 degrees

17. Classifying Angles
Complementary angles are two angles whose sum is 90 degrees
Supplementary angles are two angles whose sum is 180 degree

18. Classifying Angles
You find the complement of an angle by subtracting it’s measure from 90 degrees

19. Classifying Angles
You find the supplement of an angle by subtracting it’s measure from 180 degrees

20. Classifying Angles
Congruent Angles are angles that have the same measure

21. Classifying Angles
Adjacent angles are two angles that have the same vertex, share a common side, and do not over lap

22. Classifying Angles
Vertical angles are two opposite and equal angles formed by the intersection of two lines

23. Classifying Angles Checkpoint
Name each angle below:
1) 2)
Obtuse Angle
Acute Angle
3) 4)
Straight Angle
Right Angle or 90 degree Angle

24. Classifying Angles Checkpoint
What is the relationship between angle a and angle b?
What is the relationship between angle a and angle c?
Find the measure of angle d if angle a measures 85 degrees.
Vertical Angles
Adjacent Angles
180 – 85 = 95 degrees

25. Homework Skill 1: Lines and Angles (both sides)
Review 64 Points, Lines, Planes, and Angles (both sides)
Due tomorrow!!!