Congruent Triangles
In Plane Geometry, two objects are congruent if all of their corresponding parts
are congruent. In the first diagram, the two triangles have two sides which are
congruent, and the angle between these sides is also congruent. Euclid proved
that they are congruent triangles (Theorem I.4, called "Side-Angle-Side" of
SAS). But, he was not happy with the proof, as he avoided similar proofs in
other situations. The way he proved it, is to move one triangle until it is
superimposed on the other triangle. Such a trick (superposition: placing one
triangle on top of another, to see if they are congruent), is not considered
legal, now. It involves some complicated assumptions. So, now this (SAS) is
given as an assumption (postulate). It is the Side-Angle-Side Postulate.
are congruent. In the first diagram, the two triangles have two sides which are
congruent, and the angle between these sides is also congruent. Euclid proved
that they are congruent triangles (Theorem I.4, called "Side-Angle-Side" of
SAS). But, he was not happy with the proof, as he avoided similar proofs in
other situations. The way he proved it, is to move one triangle until it is
superimposed on the other triangle. Such a trick (superposition: placing one
triangle on top of another, to see if they are congruent), is not considered
legal, now. It involves some complicated assumptions. So, now this (SAS) is
given as an assumption (postulate). It is the Side-Angle-Side Postulate.
Their the same shape
Triangle ABC and triangle DEF have the same size and shape. If you pick up triangle ABC and put it over DEF all of the verticies and side would be the same.