Think of each angle in your shape as a hinge with no resistance. Each side is a fixed length.

A square is just a parallelogram with perpendicular sides. Those same 4 sides can be used to make any parallelogram with the same sides. There is no “invalid” point where these four sides won’t make a parallelogram, only a gradient of changing angles. It only becomes a square when the angles are all 90 degrees. That means if you push on one corner of your square, all four hinges will bend and your square becomes a different parallelogram with the same sides.

A triangle has 3 sides. Those three sides form three angles with a total of 180 degrees. For three sides of a fixed length, you can only ever make a triangle with the same angles. All the angles in between are invalid. That means when you push on the corner of your triangle, there is no gradient and your hinges don’t bend.

This is why a triangle is a strong shape. A square can be bent, a triangle has to be broken, and every useful building material on earth is harder to break than bend.

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