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 $S_1$ and $S_2$ are true

Answer 1

The correct option is A $S_1$ is true, but $S_2$ is not true.

For similarity of triangles we have SSS criteria. So $S_1$ is true.
But for polygons to be similar, the corresponding sides must be in equal ratio as well as the corresponding angles must be congruent.

Since, there is nothing mentioned about the angles of the pentagons, so $S_2$ is false.