Question

A has a pair of triangles with corresponding sides proportional, and B has a pair of pentagons with corresponding sides proportional.
$S_1\equiv$A's triangles must be similar
$S_2\equiv$ 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

Answer: (A)

$S_1$ is true, but $S_2$ is not true

Similar Polygon
Definition: 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 condition given above in the definition are independent of each other, that is either of the two condition without the other is not sufficient for polygons with more than three sides to be similar. In words, if the corresponding angles of two polygons are equal but lengths of their corresponding sides are not proportional, the polygon need not be similar. Similarly, if the corresponding angles of two polygons are not equal but lengths of their corresponding sides are proportional, the polygon need not be similar. Triangles are special type of polygons, in case of triangles if either of the two conditions holds, then the other holds automatically.