Two shapes are said to be congruent if they are the same shape and size: that is, the corresponding sides
of both shapes are the same length and corresponding angles are the same.
Shapes which are of different sizes but which have the same shape are said to be similar.
If all three sides of one triangle are the same as the lengths of the sides of the second triangle, then the two triangles are congruent.
of both shapes are the same length and corresponding angles are the same.
Shapes which are of different sizes but which have the same shape are said to be similar.
CONGRUENCE
There are four types of congruence, which are given below.1. SSS (Side, Side, Side)
2. SAS (Side, Angle, Side)
If two sides of one triangle are the same length as two sides of the other triangle and the angle between these two sides is the same in both triangles, then the triangles are congruent.
3. AAS (Angle, Angle, Side)
If two angles and the length of one corresponding side are the same in both triangles, then they are congruent.
4. Right angle, Hypotenuse, Side
If both triangles contain a right angle, have hypotenuses of the same length and one other side of the same length, then they are congruent.
SIMILARITY
They are similar because they are both Triangles and the sides of the larger triangle are two times longer than the sides of the smaller triangle.
Note
In general, if the lengths of the sides of a shape are increased by a factor k, then the area is increased by a factor k2.
