1. 1-5 Angle Relationships What are: adjacent angles linear pairs
vertical angles
complementary angles supplementary angles
perpendicular lines

2. Adjacent angles
Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points. 1 2

3. Linear Pair
A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays. 1 2

4. Definition
Two angles, , form a linear pair if and only if A, B, and C are collinear and D is not on A B C D

5. Name all the linear pairsF G H K J

6. Vertical Angles
Two angles are vertical angles if and only if their sides form two pairs of opposite rays.
OR…When two lines intersect, they form two pairs of vertical angles. 2 1 3 4

7. Definition
Complementary angles are two angles whose measures add up to 90° A B C D

8. Try it
Find the measures of 1 2 3
134°

9. Definition
Supplementary angles are two angles whose measures add up to 180° R S T U

10. Linear Pair Postulate
The angles in a linear pair are supplementary

11. What is the difference? Supplementary because it adds to 180°
AND
Linear pair because both angles are on the same line.

12. Complementary or Supplementary?
41°
49°
41°
139° P S
Angles can be complementary or supplementary regardless of their location.

13. find the measures of the angles that are complementary and supplementary to
90°− 64° = 26°
Supplementary
180°− 64° = 116°

14. Review

15. Review

16. Assignment 1-5
Page 51, 8-17,

17. Angle Relationships Day 2
What are perpendicular lines?
What can be assumed or not assumed in a drawing?

18. Perpendicular Lines
Lines, line segments or rays that form right angles are perpendicular. B A D C

19. B
Perpendicular Lines A C D

20. To Assume or Not to Assume…
In the figure, do you think you would be justified in assuming that:
B, C, and E are collinear? A B C E F G
BE ll GD? D

21. Make a List…
Make a list of rules about what you think you can and cannot assume. A B C E F G

22. What can and cannot be assumed
You May Assume:
You May Not Assume
(unless marked):
Things that look straight are straight.
Exact measurements and relative sizes of figures.
Points shown on a line are collinear.
All points shown are coplanar.
Parallel or perpendicular lines.
Relative position of points are accurate (intersection, between-ness).
Congruence

23. To Assume or Not to Assume…
Point S is between R and T.
Points R,S, and T are collinear.
Point S is the midpoint of RT.
VY<TY R S T V W Y Z

24. Assignment 1-5 Day 2
p. 52, 36-41
And worksheet 1-5