Vertical Angles Conjecture

Activity Sheet

The objectives for this activity sheet are:

  1. To determine your understanding of the Vertical Angles Conjecture. Typical geometric problems requiring the ideas of this conjecture 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 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:

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

    (Your sketch should look like this.)

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

Are you convinced?

Compass and Straight Edge Activity

  1. Use a straight edge to construct a pair of intersecting lines.
  2. Label the lines AB and CD, and the intersection point as E (see diagram above)
  3. Use a protractor to measure pairs of vertical angles.
    For example, measure the angles AEC and BED. What happens?
  4. Do the same measurements for angles AED and BEC. What happens?
  5. Construct other pairs of intersecting lines to determine if this conjecture always holds.
  6. 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

  1. x = 35
  2. y = 55
  3. z = 90

Back to the Problem Set