Overlaps

What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

Problem



If I have these two shapes:

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A square and a triangle.



and I overlap them a bit, I get this:

 

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The square and triangle overlapping.

 



The overlapped part looks like this:

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A right-angled triangle.

 

Can you match these pairs of shapes with the shape you would get if you overlapped them?

 

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Overlaps
 

For accessibility: The first pair of shapes shows two squares. The second shows a square rotated, so that it is 'balancing' upright on its corner, and a rectangle. The third pair of shapes shows 2 rectangles with their shorter side as their base. The fourth pair of shapes shows 2 rectangles standing on their longer side as their base. The fifth pair of shapes shows 2 squares, one of which is upright and the other of which is 'balancing' upright on its corner. The sixth pair of shapes shows 2 triangles, one of which is upright and the other of which is 'balancing' upright on its corner.

The possible overlap shapes are a right isosceles triangle with its right-angled corner pointing right, a longer rectangle, a shorter rectangle, a parallelogram, a square, and a right isosceles triangle with its right-angled corner pointing left.

How did you work these out?

What other interesting overlap shapes can you make using a square, a rectangle and an equilateral triangle?