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:

Solving Geometric Problems

Use the Linear Pairs Conjecture to find the missing values in the diagram below.
(Watch out! You may need the ideas from previous conjectures as well!!)


Further Investigations with Geometer's Sketch Pad

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?

Are you convinced?

Compass and Straight Edge Activity

  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.
  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?

Are you convinced?

Back: Conjectures in Geometry home page or to the List of Conjectures.
Back: Explanation of the Linear Pairs Conjecture.
Next Conjecture: Explanation of the Triangle Sum Conjecture
Next Activity: Activities for Triangle Sum Conjecture

Solutions to Problems

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

Back to the Problem Set