Congruence, Inequality On Sides of Triangles
“Congruence” concept is used to classify geometrical figures on the basis of their shapes.
WHAT IS CONGRUENCE?
In geometry, congruence refers to the similarity or equality of two geometric figures in terms of their shape and size. When two figures are congruent, it means that one can be transformed into the other through a series of rigid motions, such as translations, rotations, and reflections, without changing the size or shape of the figures. Here are the key aspects of congruence in geometry:
Corresponding Parts:
Two geometric figures are congruent if their corresponding parts (angles and sides) are equal in measure or length. This implies a one-to-one correspondence between the elements of the two figures.
Rigid Transformations:
Congruence is preserved under rigid transformations. If one figure can be obtained from another by a combination of translations (sliding), rotations (turning), and reflections (flipping), then the two figures are congruent.
Notation:
Congruence is often denoted using the symbol "\(
\cong
\)". For example, if triangle ABC is congruent to triangle DEF, it is written as \(\Delta ABC \cong \Delta DEF
\)
Criteria for Congruence:
There are different criteria for proving that two triangles or other polygons are congruent. Some common congruence criteria for triangles include:
Side-Angle-Side (SAS): If two sides and the included angle of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.
Side-Side-Side (SSS): If all three sides of one triangle are equal to the corresponding sides of another triangle, the triangles are congruent.
Angle-Side-Angle (ASA): If two angles and the included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.
Angle-Angle-Side (AAS): If two angles and a non-included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.