Lesson 4.2 Angle Measure pp. 121-126

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.

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.

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

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.

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

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°,

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

Homework pp. 124-126

■ 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

■ 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

■ 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

■ 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

■ 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

■ 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

Analytic Geometry Slopes of Lines

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.

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 =

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

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

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

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

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

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

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

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