Question

If the ratio of the corresponding sides of two triangles is equal, then to prove that the triangles are similar.​

Answer 1

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

Answer 2

Step-by-step explanation:

Well the definition of ‘similar triangles’ IS all you need.

“In geometry two triangles are similar if and only if corresponding angles are congruent and the lengths of corresponding sides are proportional. It can be shown that two triangles having congruent angles (equiangular triangles) are similar, that is, the corresponding sides can be proved to be proportional.”

Similar Triangles

There is NO need to prove what is DEFINITIONALY true. It is rather like proposing to prove that 2 + 2 = 4. Silly!

There might be a problem if you are given’ ONLY TWO angles are congruent’, or something like that, but given ‘similarity’ MEANS that the sides MUST be proportional.

Hope that helps.