On a generalization of criteria A and D for congruence of triangles

TL;DR

This paper generalizes criteria A and D for triangle congruence, providing new geometric conditions and applying them to solve specific geometric problems in planimetry.

Contribution

It introduces a broader framework for triangle congruence criteria and demonstrates their application to geometric problem solving.

Findings

Generalized criteria A and D for triangle congruence

New geometric properties characterizing non-congruent triangles

Solutions to selected geometric problems using the generalized criteria

Abstract

The conditions determining that two triangles are congruent play a basic role in planimetry. By comparing not congruent triangles with respect to given sets of corresponding elements it is important to discover if they have any common geometric properties characterizing them. The present paper is devoted to an answer of this question. We give a generalization of criteria A and D for congruence of triangles and apply it to prove some selected geometric problems.