Investigating Mathematics with GeoGebra

Henrico County Public Schools

What are the angle and diagonal relationships?

READ the instructions on the right and INTERACT with the GeoGebra applet below.

Sorry, the GeoGebra Applet could not be started. Please install Java 1.4 (or later) to use this page.

Investigation Steps

Click on the reset icon icon to reset the diagram.

 Step 1 Close 
  1. Observe the measures of CE, BE, DE, and AE.

  2. What can you say about the diagonals CB and AD?

  3. Move points A, C, or B.

  4. Do your observations hold true for all parallelograms?

 Step 2 Close 
  1. Observe ∠AEB and ∠CED. What do you notice?

  2. Observe ∠AEC and ∠BED. What do you notice?

  3. Move points A, C, or B.

  4. Do your observations hold true for all parallelograms?

  5. Write your observations in the form of a conjecture.

 Check ConjecturesClose 
  1. Most of the time the diagonals are not congruent.

  2. The diagonals bisect each other.

  3. The angles formed by the intersection of the diagonals vary.