Congruence Of Triangles

If we superpose one triangle over other triangle and they cover each other properly, then they must be congruent triangles.

In case of congruent triangles-

  • All the sides of one triangle must be equal to the corresponding sides of another triangle.
  • All the angles of one triangle must be equal to the corresponding angles of another triangle.
  • All the vertices of one triangle must be corresponding to the vertices of another triangle.

In the above triangles,

If, ∆ABC ≅ ∆FDE then

  • Corresponding vertices are – ∠A ↔ ∠F, ∠B ↔ ∠D and ∠C ↔ ∠E
  • Corresponding angles are – ∠A ↔ ∠F, ∠B ↔ ∠D and ∠C ↔ ∠E
  • Corresponding sides are – AB ↔ FD, BC ↔ DE and AC ↔ FE

Remark: It is the order of the letters in the names of congruent triangles which tells the corresponding relationships between two triangles. If we change it from ∆ABC ≅ ∆FDE to ∆BCA ≅ ∆FDE, then it is not necessary that the two triangles are congruent as it is important that all the corresponding sides, angles and vertices are same.

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