• Two geometric figures are congruent if they have the same shape and the same size.
Corresponding parts of congruent triangles are congruent (equal) (c.p.c.t.c) i.e.,if ΔABC ≅ ΔPQR then ∠A = ∠P, ∠B = ∠Q, ∠C = ∠ R, AB = PQ, BC = QR and AC = PR.
There are five congruence criterion:
1. SAS
2. ASA
3. AAS
4. SSS
5. RHS
1.By SAS rule, 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.
2.By ASA 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.
3. By AAS rule, if two angles and any one side of one triangle are equal to two angles and corresponding side of the other triangle, then the two triangles are congruent.
4. By SSS rule, if three sides of one triangle are equal to three sides of the other triangle then the two triangles are congruent.
5. By RHS rule, if in two right angled triangle, one side and the hypotenuse of a triangle are equal to one side and the hypotenuse of the other triangle then the two triangles are congruent.
• In a triangle
Angles opposite to equal sides are equal.
Sides opposite to equal angles are equal.
Angles opposite to the longer side is greater.
Side opposite to the greater angle is longer.
Sum of any two sides is greater than the third side.
Difference of any two sides is always less than the third side.