Zig Zag

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Congratulations Soh Yong Sheng of Raffles Institution, Singapore and James of Hethersett High School for your solution. The image

can be further expanded into a diagram containing 3 squares of which two are the same size.

The two smallest quadrilaterals produced are squares as their sides are all of the same length equal to the shortest side of the triangle. The dots will form one line containing the diagonals of the three squares as the sides of the squares are all perpendicular or parallel to each other.

Here is another way of looking at it.