# Vertical Angles Conjecture

Activity Sheet

### The objectives for this activity sheet are:

- To determine your understanding of the Vertical Angles Conjecture. Typical geometric problems requiring the ideas of this conjecture 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 Vertical Angle Conjecture to find the missing values in the diagram below.
solutions.

## Further Investigations with Geometer's Sketch Pad

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

- Construct two lines which meet at a single point. Lines AB and CD.
- Construct a point at the intersection of these two lines. Give this point the label "E".

(Your sketch should look like this.)

- Measure the angles AEC and BED by selecting the points and using the Measure Menu.
- Compare the two measurements. What do you find?
- Drag the points A, B, C, and D to see what happens to the angle measurements.
- Do the same for the angles AED and BEC. What happens?

### Are you convinced?

## Compass and Straight Edge Activity

- Use a straight edge to construct a pair of intersecting lines.
- Label the lines AB and CD, and the intersection point as E (see diagram above)
- Use a protractor to measure pairs of vertical angles.

For example, measure the angles AEC and BED. What happens?
- Do the same measurements for angles AED and BEC. What happens?
- Construct other pairs of intersecting lines 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
Vertical Angles Conjecture.

**Next Conjecture: ** Explanation of the Linear Pairs Conjecture

**Next Activity: ** Activities for Linear Pairs Conjecture

### Solutions to Problems

- x = 35
- y = 55
- z = 90

Back to the Problem Set