SAS and SSA Conditions for Congruent Triangles

Abstract

For two triangles to be congruent, SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle. If the congruent angles are not between the corresponding congruent sides, then such triangles could be different. It turns out that it is possible to describe four cases in which triangles are congruent even though congruent angles. For two triangles to be congruent, SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle. If the congruent angles are not between the corresponding congruent sides, then such triangles could be different. It turns out that it is possible to describe four cases in which triangles are congruent even though congruent angles are not between the corresponding congruent sides. Such a theorem could be named, for example, SSA theorem. Many texts state that two triangles cannot be shown to be congruent if the condition of SSA exists. However, the author describes cases in which such triangles could be proven congruent with the SSA theorem. An immediate consequence of this new understanding is the necessity of revising many problems and answers in high school and college-level texts related to congruent triangles.are not between the corresponding congruent sides. Such a theorem could be named, for example, SSA theorem. An immediate consequence of this new understanding is the necessity of revising many problems and answers in high school and college-level texts related to congruent triangles.