Question

All squares are similar.
A. True
B. False

Answer 1

Hint: In the given question, we have been asked that the given statement is true or false and the statement is that all the squares are similar. In order to answer this question, first we need to take any two squares of each having different measures of side and finding the ratios of their corresponding sides. If the ratios of corresponding parts are equal then consequently the figures are similar.

Complete step by step solution:
We have given that,
All squares are similar.
Two figures can be said to be similar when they are having the same shape but it is not always necessary to have the same size.
Yes, we can say that all squares are equal. The size of every square may not be the same or equal but the ratios of their corresponding sides or the corresponding parts are always equal. All the angles of each square are 90 degrees.
Let’s take two squares ABCD and PQRS
As we know that all sides of a square are equal.
Square ABCD having a side of 4cm and square PQRS is a square having a side of 12 cm.

Consider the square ABCD and PQRS shown in the above figures;
The ratio of their corresponding sides are,
\[\dfrac{AB}{PQ}=\dfrac{4}{12}=\dfrac{1}{3}\]
\[\dfrac{BC}{QR}=\dfrac{4}{12}=\dfrac{1}{3}\]
\[\dfrac{CD}{RS}=\dfrac{4}{12}=\dfrac{1}{3}\]
\[\dfrac{AD}{PS}=\dfrac{4}{12}=\dfrac{1}{3}\]
As the ratios of their corresponding sides are equal. Hence the two squares are similar.
Similarly all squares are similar.

Thus, the given statement is true and hence the option (a) is correct.

Note: While solving the answer to this question, students need to remember the properties of square i.e. all the sides of a square are equal, all the angles of the square are 90 degrees. It is important to know the difference between the word equal and similar, the question is asking whether all the squares are equal or not. Similar figures are those figures which are similar in shape but not necessary to have the same size and the ratio of their corresponding parts is equal, then they are similar.