Question

A has a pair of triangles with corresponding sides proportional, and B has a pair of pentagons with corresponding sides proportional.

$S_1$ - A’s triangles must be similar.

$S_2$ - B’s pentagons must be similar.

Which of the following statement is correct?

• A. $S_1$ is true but $S_2$ is not true.
• B. $S_2$ is true but $S_1$ is not true.
• C. Both $S_1$ and $S_2$ are true.
• D. Neither $S_1$ nor $S_2$ is true.

Answer 1

The correct option is A

$S_1$ is true but $S_2$ is not true.

Two polygons are said to be similar to each other if

1) their corresponding angles are equal, and

2) the lengths of their corresponding sides are proportional

It should be noted that for the similarity of polygons with more than three sides, the two conditions given above in the definition are independent of each other, i.e., either of the two conditions without the other is not sufficient for polygons with more than three sides to be similar. In other words, if the corresponding angles of two polygons are equal but lengths of their corresponding sides are not proportional, the polygons need not be similar. Similarly if the corresponding angles of the two polygons are not equal but lengths of their corresponding sides are proportional, the polygons need not be similar.

Triangles are special type of polygons with three sides. In case of triangles, if either of the two conditions holds, then the other holds automatically.