Try these activities to stimulate students’ conjectures. Created with GeoGebra, by Hee-Joon Kim.


Inscribed Square

inscribed square

The figure ABCD is a square. The figure EFGH is a square inscribed in the square ABCD. 

  1. Move the point E along the side AB. What do you notice? 
  2. Make a conjecture about the inscribed square EFGH. 


Reflection on a Coordinate Plane

ABC triangle

The triangle A’B’C’ is an image of the triangle ABC after reflection across the red line. 

  1. Move the line of reflection either by dragging the line or moving the black points on the line. What do you notice?  
  2. Make a conjecture about relationships between the preimage and the image after the reflection.

For further exploration and conjecturing, look at coordinates or ancillary segments.