Dissection Process

Below are the construction steps to dissect an equilateral triangle into pieces that can be reassembled into a rectangle.

Step 1 is to divide the base into four equal parts and construct the midpoints of the other two sides.

Step 2 is to construct the line segment joining one of the midpoints to the far quarter point of the base.

Step 3 is to construct perpendiculars from the 'other' midpoint and 'other' quarter point to the segment constructed in step 2.

The quadrilaterals 1, 2, and 3 and triangle four shown to the right form the dissection. A way to show that they can be reassembled into a rectangle starts with a 180 degree rotation of polygons 2, 3, and 4 about midpoint A. Can you show whether the rectangle formed is a square?

MAIN DISSECTION PAGE

Step 1 is to divide the base into four equal parts and construct the midpoints of the other two sides.
Step 2 is to construct the line segment joining one of the midpoints to the far quarter point of the base.
Step 3 is to construct perpendiculars from the 'other' midpoint and 'other' quarter point to the segment constructed in step 2.
The quadrilaterals 1, 2, and 3 and triangle four shown to the right form the dissection. A way to show that they can be reassembled into a rectangle starts with a 180 degree rotation of polygons 2, 3, and 4 about midpoint A. Can you show whether the rectangle formed is a square?