Linear Pairs Conjecture

Activity Sheet

The objectives for this activity sheet are:

1. To determine your understanding of the Linear Pairs Conjecture. Typical geometric problems requiring the ideas of this conjecture, coupled with ideas from previous conjectures, are given for you to solve.

2. To give you the opportunity to explore this conjecture further through construction activities involving:
   
   • Geometer's Sketch Pad
   • Compass and Straight Edge

Directions: Open the Geometer's Sketch Pad program on your computer. Then follow these directions:

1. Construct a line AB which is approximately horizontal.
2. Construct a ray CD which begins at a point on the line between points A and B.
   
   (Your sketch should look like this.)

3. The angles ACD and BCD are an example of a linear pair of angles.
4. Measure the angles ACD and BCD by selecting the points and using the Measure Menu.
5. Add the measures of these two angles by selecting each of them, and using the Measure/Calculate Menu.
6. Drag the point D and note what happens to the sum of the angle measurements.
7. What happens?

1. Use a straight edge to construct a horizontal line AB on your paper.
2. Pick a point C on the line somewhere between the points A and B
3. Construct a ray from the point C through another point D which is not on the line.
   The angles ACD and BCD are an example of a linear pair of angles.
4. Use a protractor to measure the linear pair of angles. Record these values.
   • Angle ACD = ????
   • Angle BCD = ????
5. Add the results of your measurements. What number do you get? Is it 180?
6. If you did not get a total of 180, what do you think happened?

7. Construct other linear pairs to determine if this conjecture always holds.
8. What happens?

1. a = 145
2. b = 35
3. c = 55
4. d = 125
5. e = 125
6. f = 90
7. g = 90