# Linear Pairs Conjecture

Activity Sheet

### The objectives for this activity sheet are:

- 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.

- To give you the opportunity to explore this conjecture further through construction activities involving:

- Geometer's Sketch Pad
- Compass and Straight Edge

## 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!!)
solutions.

## Further Investigations with Geometer's Sketch Pad

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

- Construct a line AB which is approximately horizontal.
- Construct a ray CD which begins at a point on the line between points A and B.

(Your sketch should look like this.)

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

### Are you convinced?

## Compass and Straight Edge Activity

- Use a straight edge to construct a horizontal line AB on your paper.
- Pick a point C on the line somewhere between the points A and B
- 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.
- Use a protractor to measure the linear pair of angles. Record these values.
- Angle ACD = ????
- Angle BCD = ????

- Add the results of your measurements. What number do you get? Is it 180?
- If you did not get a total of 180, what do you think happened?

- Construct other linear pairs to determine if this conjecture always holds.
- 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

- a = 145
- b = 35
- c = 55
- d = 125
- e = 125
- f = 90
- g = 90

Back to the Problem Set