Angle Relationships and Parallel Lines
Angle Relationships and Parallel Lines
Angle Relationships and Parallel Lines
Introduction to Angles
Activity 1: Definitions 1.) What is an angle? Define it as best you can below.
Activity 2: Protractors 1.) Lets look at how to measure different angles with protractors. a. Grab a protractor and measure the angle:
3.) Here are the two angles combined: a. Whats the measure of the two angles added together?
b. Why?
4.) Two angles that, when added equal a straight line, or 180 degrees are called supplementary. What angle is supplementary to each of the angles below? a. 70:______ d. 35:______ g. 64.25:______ b. 50:______ e. 90:______ h. 0.04:______ c. 20:______ f. 2:______ i. x:_________
Activity 3: Some angle relationships. 1.) Measure all four angles in the figure to the right. a. b. c. d. 2.) Did you notice any interesting patterns?
2 3 4
3.) Lets try again. Measure all four angles in the figure to the right. a. b. c. d. 4.) Did you notice any interesting patterns?
2 3
1 4
5.) Angles that are formed by two intersecting lines and are directly opposite each other are called vertical angles. So for example, and are vertical angles and and are vertical angles in each of the above diagrams. What relationship do vertical angles seem to have?
6.) Use what you just figured out. Without a protractor, find angles a.
and
145 2 3
b. c.
Activity 4: Some more angle relationships. Things get pretty interesting if we add in another line parallel to one of the lines already there. 1.) Measure each of the angles in the figure: a. b. c. d. e. f. g. h.
5 7 8
Activity 5: The line crossing through the parallel lines is called a transversal. Whenever a transversal cuts through two parallel lines, it forms 4 pairs of vertical angles- two pairs that are equal to each other and are supplementary to the other two pairs of equal vertical angles. This always holds true. See if you can use these relationships to answer the questions below. 1.) Using the diagram, find the measure of the angles: a. b. 2 1 6 5 c. 3 7 4 112 d. e. f. g. 2.) Using the diagram, find the measure of the angles: a. 2 b. 1 c. 3 4 d. e. f. 5 6 84 g. 7
Homework
1.) How many degrees are in a full circle? 2.) How many degrees are in half a circle? 3.) How many degrees are in a quarter of a circle? 4.) How many degrees are in an eighth of a circle?
128 B C A
A 54 B
A 134
65 Z
D
10.) Find the measure of angle D
107
X
11.) Find the measure of angles X, Y and Z a. b. c.
42 Y Z
29