Congruence of triangles

Triangles " égaux" or isometric triangles.

In a more current language, two triangles are known as isometric when measurements on their sides are two to two equal. Practically that means that these triangles are superposable. One can show that two isometric triangles are in fact the image one of the other by a Isométrie of the plan.

First characterization

Theorem: if two triangles have a of the same side length ranging between two angles of same measurements, then these triangles are isometric.

Second characterization

Theorem: if two triangles have an of the same angle measures included/understood between two of the same sides length, then these triangles are isometric.

Note:: the preceding theorem can spread: the common angle does not need necessarily to be between the two common sides so that the two triangles are isometric. Indeed, two segments and an angle define a single triangle (except for isometry).

Properties

Two isometric triangles are similar Triangles. Moreover their surfaces are equal.

Random links: