Basically, if two shapes are congruent, they are the same (shape and size). It is often useful to know whether two triangles are congruent.

Two triangles are congruent if any one of the following is true:

• All three sides of one triangle are the same length as all three sides of the other triangle (i.e. a = d, b = f and c = e below).
  

• Two of the angles and a side of one triangle are equal to the corresponding two angles and side of the other triangle (e.g. A = D, C = E and a = d) .
  

• An angle between two sides of a triangle is equal to the corresponding angle in the other triangle and the sides in question are equal (e.g. C = E, b = f, a = d)
  

• Two right angled triangles have the same hypotenuse and one other equal side.

Copyright © Matthew Pinkney 2003