You may also like

problem icon

Pareq Exists

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

problem icon

The Medieval Octagon

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

problem icon

Folding Squares

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

Triangle Midpoints

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Given the three midpoints of the sides of a triangle, can you find a way to construct the original triangle?

For example:


Choose any three points.
Can you construct a triangle such that your three points are the midpoints of its sides?

Is there more than one possible triangle for any given set of midpoints?