Congruent

Congruent

Angles and triangles

Published in John Bird, Basic Engineering Mathematics, 2017

Two triangles are said to be congruent if they are equal in all respects; i.e. three angles and three sides in one triangle are equal to three angles and three sides in the other triangle. Two triangles are congruent ifthe three sides of one are equal to the three sides of the other (SSS),two sides of one are equal to two sides of the other and the angles included by these sides are equal (SAS),two angles of the one are equal to two angles of the other and any side of the first is equal to the corresponding side of the other (ASA), ortheir hypotenuses are equal and one other side of one is equal to the corresponding side of the other (RHS).

Students' conceptions of the definitions of congruent and similar triangles

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Journal Information

Published in International Journal of Mathematical Education in Science and Technology, 2022

Aehsan Haj-Yahya

Vinner (1991) mentioned that in the classroom, mathematics teachers might develop a sequence of definitions, theorems and proofs as a framework for mathematics courses. The same conceptual framework can be used with congruent and similar triangles. After proving the congruent and similar triangles theorems and highlighting the necessary and sufficient conditions of these theorems, teachers can use these theorems to solve problems. They can use them to identify, classify, and prove congruent and similar triangles. That is, these theorems fulfil the role of definitions with regard to these concepts (Moore, 1994; Vinner, 1991; Weber, 2002).

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Angles and triangles

Students' conceptions of the definitions of congruent and similar triangles