Try these activities to stimulate students’ conjectures. Created with GeoGebra, by Hee-Joon Kim.
Inscribed Square
The figure ABCD is a square. The figure EFGH is a square inscribed in the square ABCD.
- Move the point E along the side AB. What do you notice?
- Make a conjecture about the inscribed square EFGH.
Reflection on a Coordinate Plane
The triangle A’B’C’ is an image of the triangle ABC after reflection across the red line.
- Move the line of reflection either by dragging the line or moving the black points on the line. What do you notice?
- 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.