Important point about congruent triangles:
(1) Two congruent triangles are surely equiangular but equiangular triangles need not be congruent. We do not have a condition like AAA criterion for congruence of triangles.
(2) If two triangles are congruent, then they are similar. Its converse is not true. In triangle ABC and DEF.
(3) = a constant = k (say)
When k = 1, we get congruent figures and also similar, image is similar to pre image.
The ratio of corresponding sides is k.
The corresponding sides are parallel to each other.
The ratio of the areas of two similar figures is k2.
In solids, the ratio of the volumes of two similar solids will be k3.
(4) The order of letters in the names of the two triangles also indicates the correspondence between the vertices of the two triangles. We will adopt this convention. Then from the manner the two triangles are named, we can easily infer the six equalities between the corresponding parts of the two congruent triangles, (Abbreviated as C.P.C.T.)
(5) Congruent triangles coincide on superposition.
(6) In congruent triangles corresponding sides lie opposite equal angles and corresponding angles lie opposite equal sides.
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