Congruent triangles

If two triangles are congruent they must have the same shape and the same size.

This means that they will fit exactly onto each other when one of the m is rotated, reflected or translated.

Two triangles are congruent if any of these conditions are satisfied.

(i) SAS (side, angle, side) postulate:

Two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.

In the above triangles ΔABC and ΔDEF,

AB=DE ( side)

∠A = ∠D(included angle)

AC = DC (side)

By SAS postulate ΔABC ≅ ΔDEF, Read ≅ as Congruent

(ii) SSS postulate (side, side, and side)

The three sides of one triangle are equal to the corresponding three sides of the other triangle.

In these two triangles,

AB = DE (side)

AC = DF (side)

BC= EF (side)

By SSS postulate,

ΔABC ≅ ΔDEF

(iii) AAS postulate: (angle, corresponding angle side)

Two angles and a side in one triangle are equal to two angles and the corresponding side in the other triangle

Here in these two triangles,

∠A = ∠D (angle)

∠C = ∠F (corresponding angle)

AC = DF (side)

By AAS postulate,

ΔABC ≅ ΔDEF

(iv) RHS postulate: (right angle, hypotenuse, side)

Each triangle is right angled and the hypotenuse and one side of one triangle is equal to the hypotenuse and a side of the other triangle.

Here in these two triangles,

∠A = ∠D = 90°

CB=FE ( hypotenuse)

AC = DF ( one side)

By RHS postulate,

ΔABC ≅ ΔDEF

Answer the following:

1. Which of the following pairs of triangles are congruent?

(a)

(b)

(c)