Question

Two polygons of the same number of sides are similar, if (a) their corresponding angles are ______ and (b) their corresponding sides are ______.
(A) equal, proportional
(B) proportional, equal
(C) equal, equal
(D) None of these

Answer 1

Hint: We start solving this question by first starting with going through the definition of similarity of the polygons. Then using the definition, we answer the question as required and mark the answer to the question.

Complete step-by-step solution:
The common way of defining the Similarity of polygons is,
Any two polygons are said to be similar if they are of the same shape and they can be of different sizes.
The Mathematical definition is,
Any two polygons are said to be similar if they satisfy the below two conditions.
1) The corresponding sides of both the polygons are in the same proportion.
2) The corresponding interior angles of the polygons are the same.
For example, consider the two polygons below.

As we see these polygons their corresponding angles are the same and their sides are in the same proportion. So, the above polygons are similar.
We are asked to find the when two polygons of the same number of sides are similar if their corresponding angles are ______ and their corresponding sides are ______.
From the above definition of similar polygons, we can say that,

Two polygons of the same number of sides are similar if their corresponding angles are equal and their corresponding sides are proportional. Hence answer is Option (A).

Note: There is a possibility of one making a mistake of answering that two polygons of the same number of sides are similar if their corresponding angles are proportional and their corresponding sides are equal, by confusing the definition between angles and sides in reverse and write the answer as Option B. But if the angles are proportional then the shape of the polygon changes and so they don’t look similar. So, one needs to remember the definitions clearly and perfectly.