Vertical Angles Conjecture
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.
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