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
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Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


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.