# Quadrilateral Sum Conjecture

Activity Sheet

### The objectives for this activity sheet are:

- To determine your understanding of the Quadrilateral Sum 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 Quadrilateral Sum Conjecture to find the missing values in the diagram below.

(Watch out! You may will 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 convex quadrilateral ABCD with four line segments: AB, BC, CD, and DA.

(Your sketch should look like this.)

- Measure each angle using the Measure Menu. Record each of these values.
- Angle ABC = ??
- Angle BCD = ??
- Angle CDA = ??
- Angle DAB = ??

- Add the measures of these four angles by selecting each of them, and using the Measure/Calculate Menu. What is the sum of their measures?
- Use the mouse to drag any of the vertices of the quadrilateral. Note what happens to the sum of the angle measurements.
- What happens?
- What happens if you drag a vertex so that the quadrilateral does not remain convex?

### Are you convinced?

## Compass and Straight Edge Activity

- Use a straight edge to construct any quadrilateral ABCD.
- Use a protractor to measure each of the four angles.
- Find the sum of the four angle measurements. What do you get?
- If you did not get a total of 360, what do you think happened?

- Try constructing another quadrilateral, perhaps one with a different shape to it. Measure each angle and find the total again.
- What do you get? Do you get 360? if not, are you close?

### Are you convinced?

**Back:** Conjectures in Geometry home page or to the List of Conjectures.

**Back:** Explanation of the
Quadrilateral Sum Conjecture.

**Next Conjecture: ** Explanation of the Polygon Sum Conjecture

**Next Activity: ** Activities for Polygon Sum Conjecture

### Solutions to Problems

- A = 87
- B = 93
- C = 140
- D = 20
- E = 120
- F = 60
- G = 67
- H = 65
- J = 67
- K = 113
- L = 120
- M = 77
- N = 60

Back to the Problem Set