Investigating Mathematics with GeoGebra

Henrico County Public Schools

Under what conditions is a rhombus a square?

READ the instructions on the right and INTERACT with the GeoGebra applet below.
Click on the reset icon icon to reset the diagram.

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

Investigation Steps

 Step 1 Close 
  1. Move point A, C, or B. Observe the measure of sides of the figure. What do you notice?

  2. Use the angle tool angle tool to measure ∠DCB and ∠BAD

  3. Move point A, C, or B. Observe the measures of the opposite angles of your rhombus.

  4. Do your observations hold true for all rhombi?

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

 Step 2 Close 
  1. Control Click on each segment AE, DE, CE, and BE and change the properties to show their value.

  2. Observe the measures of AE, DE, CE, and BE.

  3. What can you say about the diagonals AC and DB? Move point A, C, or B.

  4. Do your observations hold true for all rhombi?

 Step 3 Close 
  1. Use the angle tool angle tool to measure ∠AEB and ∠CED. What do you notice?

  2. Move point A, C, or B so that ∠AEB and ∠CED are 90°.

  3. What do you call this figure?

  4. Move point A, C, or B. Do your observations hold true for all rhombi?

 Check ConjecturesClose 
  1. All sides are equal.
  2. Opposite angles are equal.
  3. Opposite sides are parallel.
  4. Diagonals are perpendicular bisectors of each other.
  5. Rhombus with all angles equal to 90° is called a square.