Triangles

No matter what shape a triangle takes, its three interior angles always add to 180° — and you can see exactly why by tearing the corners off.

Extend one side of a triangle and a new angle appears outside it — and it equals the two far-off interior angles added together.

Join the midpoints of two sides of a triangle and you get a segment that is parallel to the third side and exactly half as long.

Three lengths only close into a triangle when any two of them, added together, beat the third — otherwise the short sides can't reach across to meet.

Give a triangle two equal sides and its two base angles come out equal too — and the rule runs both ways.