Question

explain the 4th axiom of Euclid

Answer 1

Euclid’s Fourth Axiom: Coincidental Equality

The fourth axiom seems to be the most obvious reference to geometry. If two shapes “coincide,” then one fills out the exact shape and volume of the second.

Simple cases include angles that are equal, straight line segments of the same length, and triangles of the same size and shape.

Consider drawing a triangle, and then constructing a second triangle in a way that copies the angles and lengths from the first triangle. Then, cut out the second triangle and lay it over the first. If these triangles precisely overlap, then they “coincide,” and are equal to one another.