Similar Triangles Formula
Similar triangles formulas are used in confirming whether the given triangles are similar or not. Two figures are said to be similar if one figure can be obtained from another by a sequence of transformations such as resizing, flipping, sliding, or turning. That is, similar figures have the same shape but not necessarily the same size. Let us understand the similar triangles formula in detail in the following section.
What Are the Formulas for Similar Triangles?
Two triangles are said to be similar if their:
 corresponding angles are equal
 corresponding sides are in the same ratio
However, to ensure that the two triangles are similar, we do not necessarily need to have information about all sides and all angles.
There are three criteria/formulas to determine if two triangles are similar.
 AA (Angle Angle): If any two of the angles of the triangles are equal, then the triangles are said to be similar.
 SAS (Side Angle Side): If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.
 SSS (Side Side Side): If two triangles have three pairs of sides in the same ratio, then the triangles are similar.
The symbol used to denote the similarity between triangles is '~'. Triangles ABC and DEF are similar is denoted by △ABC∼△DEF.
Let us have a look at a few solved examples to understand similar triangles formulas better.
Solved Examples Using Similar Triangles Formula

Example 1: The dimensions of triangles ABC and DEF are as follows:
AB = 4 units, BC = 5 units, AC = 6 units
DE=16 units, EF=20 units, DF=24 units
Using similar triangles formulas, check if the triangles are similar.
Solution:
Determine the ratio of the corresponding sides of the triangles to check if they are similar.
Take the ratio of the shortest sides of both the triangles and the ratio of the longest sides of both the triangles.
AB/DE = 4/16 = 1/4
BC/EF = 5/20 = 1/4
AC/FG = 6/24 = 1/4
Using similar triangles formulas, we conclude that since the corresponding sides of the triangles are in the same ratio, therefore they are similar.
Answer: △ABC∼△DEF

Example 2: Is every pair of equilateral triangles similar?
Solution:
The measure of each angle in an equilateral triangle is 60^{∘}.
Using similar triangles formulas, we conclude that since the corresponding angles in every pair of the equilateral triangle are equal to 60^{∘}, the triangles are similar.
Answer: Yes, every pair of equilateral triangles is similar.