Congruence, Inequality On sides of Triangles

Congruence, Inequality On sides of Triangles

Congruence Relations:
(i) Reflex Relation : Every triangle is congruent to itself  i.e. \( \Delta ABC \cong \Delta ABC \)
(ii) Symmetric Relation : If \( \Delta ABC \cong \Delta DEF \) then \( \Delta DEF \cong \Delta ABC \)
(iii)Transitive relations : If \( \Delta ABC \cong \Delta DEF \) and \( \Delta DEF \cong \Delta PQR \), then \( \Delta ABC \cong \Delta PQR \).
hence, congruency relation is “ an equivalence relation”.

Congruence Criterion : In order or to prove that two triangles are congruent,we have the following     criterions.
(i) Side - Angle - Side (SAS)
(ii)Angle-Side -Angle(ASA)
(iii)Angle-Angle-Side (AAS)
(iv) Side-side-side (SSS)
(v) Right Angle-Hypotenuse-side(RHS)