Monthly Archives: June 2014

How many isosceles trapeziums?


In Mathematics, an isosceles trapezium is a quadrilateral one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.

How many isosceles trapeziums do you count in this figure?
Matchsticks 4x4 triangles

Just for the sake of clarity, three triangles in one row would make an isosceles trapezium, as the red one in this example:
triangles isosceles trapeziums

You can check your solution at here

Please try to solve the puzzles on your own: your self confidence will grow. You are welcome to remark on the puzzles, and I love it when you comment variations, state wether they are too easy or too difficult, or simply your solution times. Please do not state the soultions – it spoils the fun for others. I usually make the solution available after one or two weeks through a link, which allows readers to check the solution without the temptation to scroll down a few lines before having a go at it themselves.