Right-Angled Request

Weekly Problem 26 - 2006
How many right angled triangles are formed by the points in this diagram?
Age
11 to 14
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Right-Angled Request


The figure shows a rectangle PRSU with a line QT, which divides the rectangle into two squares.
How many right-angle triangles can be drawn using any three points P, Q, R, S, T, U as corners?
 


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.