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Summary

  • Two figures are congruent, if the shape and size are same.
  • If two triangles ABC and PQR are congruent under the correspondence

A P, B Q and C R, then symbolically, it is expressed as Δ ABC Δ PQR.

  • If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent (SAS Congruence Rule).
  • If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent (ASA Congruence Rule).
  • If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent (AAS Congruence Rule).
  • Angles opposite to equal sides of a triangle are equal.
  • Sides opposite to equal angles of a triangle are equal.
  • If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent (SSS Congruence Rule).
  • If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent (RHS Congruence Rule).
  • In a triangle, angle opposite to the longer side is larger (greater).
  • In a triangle, side opposite to the larger (greater) angle is longer.
  • Sum of any two sides of a triangle is greater than the third side.




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