1. Lesson 4.2
Angle Measure pp

2. Objectives:
1. To state the Protractor and Continuity Postulates.
2. To use a protractor to measure and draw angles.
3. To classify angles by their angle measure.
4. To define congruent angles.

3. Postulate 4.1
Protractor Postulate. For every angle A there corresponds a positive real number less than or equal to 180. This is symbolized 0  mA  180.

4. Definition
The measure of an angle is the real number that corresponds to a particular angle.

5. Postulate 4.2
Continuity Postulate. If k is a half-plane determined by AC, then for every real number,
0  x  180, there is exactly one ray, AB, that lies in k such that mBAC = x.

6. Angle name Angle measure
Acute angle 0° < x < 90°
Right angle x = 90°
Obtuse angle 90° < x < 180°
Straight angle x = 180°

7. Definition Congruent angles are angles that have the same measure. A B
50° A B C X Y Z
mABC = 50° & mXYZ = 50°,

8. Definition Congruent angles are angles that have the same measure. A B
50° A B C X Y Z
so ABC  XYZ.

9. Homework pp

10. ■ Cumulative Review 26. What do we call surfaces in A  B?
Answer the questions about the Venn diagram below.
A = The set of
cylinders
B = The set of
polyhedra
C = The set of cones
26. What do we call surfaces in A  B? A B C
Surfaces

11. ■ Cumulative Review 27. What do we call surfaces in B  C?
Answer the questions about the Venn diagram below.
A = The set of
cylinders
B = The set of
polyhedra
C = The set of cones
27. What do we call surfaces in B  C? A B C
Surfaces

12. ■ Cumulative Review 28. A  B
Give an example of a surface in each set below.
A = The set of
cylinders
B = The set of
polyhedra
C = The set of cones
28. A  B A B C
Surfaces

13. ■ Cumulative Review 29. C  B
Give an example of a surface in each set below.
A = The set of
cylinders
B = The set of
polyhedra
C = The set of cones
29. C  B A B C
Surfaces

14. ■ Cumulative Review 30. B  (A  C)
Give an example of a surface in each set below.
A = The set of
cylinders
B = The set of
polyhedra
C = The set of cones
30. B  (A  C) A B C
Surfaces

15. ■ Cumulative Review 31. (A  B  C)
Give an example of a surface in each set below.
A = The set of
cylinders
B = The set of
polyhedra
C = The set of cones
31. (A  B  C) A B C
Surfaces

16. Analytic Geometry
Slopes of Lines

17. Analytic Geometry Slopes of Lines
You can measure steepness in two ways. One way is to find the angle on inclination above the horizontal using a protractor. The other way is to calculate a number called the slope.

18. Definition
The slope of a line is the ratio obtained from two points of a line by dividing the difference in y coordinates by the difference in x coordinates. m 1 2 x - y =

19. Give the slope of the line passing through (9, -7) and (-4, -2).
m =
-4 – 9
-2 – (-7) 5
-13 = 13 -5 =

20. Give the slope of the line passing through (-5, 1) and (6, -3).

21. ►Exercises
Give the slope of the line passing through
1. (0, 0) and (3, -2).

22. ►Exercises
Give the slope of the line passing through
2. (-2, 3) and (2, 4).

23. ►Exercises
Give the slope of the line passing through
3. (6, -2) and (5, 3).

24. ►Exercises
Give the slope of each line shown. 4.

25. ►Exercises
Give the slope of each line shown. 5.

26. Give the slope of the line shown.x y
run
rise