Answer: The correct option is
(A) The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.
Step-by-step explanation: We are given to select the correct condition that might be true if polygons ABCD and KLMN are similar.
Two polygons are said to be SIMILAR if corresponding angles are congruent and corresponding sides are proportional.
So, options (B), (C), (D) and (E) are not correct because they contradict conditions of similarity.
In option (A), we have
The measures of corresponding angles of ABCD and KLMN are equal. So, they must be congruent.
And the lengths of corresponding sides of ABCD are half those of KLMN.
So, we can write
[tex]AB=\dfrac{1}{2}KL,~~BC=\dfrac{1}{2}LM,~~CD=\dfrac{1}{2}MN,~~AD=\dfrac{1}{2}KN\\\\\\\Rightarrow \dfrac{AB}{KL}=\dfrac{BC}{LM}=\dfrac{CD}{MN}=\dfrac{AD}{KN}=\dfrac{1}{2}.[/tex]
Therefore, the corresponding sides are proportional.
Thus, option (A) is true if two polygons are similar.
