1. Line and Angle Relationships

2. 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
Lines continue infinitely in both directions while a line segment has 2 endpoints
A B
AB, “line AB”
AB, “line segment AB”

4. Points, Lines, and Rays
A ray is the part of a line that extends without end in one direction
A B C
In AB, “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 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 or Plane BCDA… A B
D C

6. Points, Lines, and Rays Checkpoint
Look at the line below:
A B C
Name a line segment
Name a ray in two different ways
What is the endpoint of ray BC?
AB, AC, BA, BC, CB, and CA
AB and AC or CB and CA
Point 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
Point B is the common endpoint or vertex
Instead of using the word angle, you can use the symbol for angle, which is

9. Naming Angles There are two 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)
If only given the vertex then 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
Point Y
XYZ, XYW, and WYZ

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

13. Classifying Angles An obtuse angle measures greater than 90º
A straight angle measures exactly 180º

14. Classifying Angles
A reflex angle measures greater than 180º

15. Classifying Angles
Complementary angles are two angles whose sum is 90º
Supplementary angles are two angles whose sum is 180º

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

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

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

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

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

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

22. 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 85º.
Vertical Angles
Adjacent Angles, supplementary angles
180º – 85º = 95º

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