Answer: The correct option is (B) HB = HB'.
Step-by-step explanation: Given that polygon ABCD is reflected across EF to make polygon A'B'C'D'.
We are to select the correct statement from the given options.
Since EF is the line of reflection, so the distance of each vertex of the original polygon ABCD is equal to the distance of the corresponding vertex of the reflected polygon A'B'C'D'.
That is,
The corresponding vertex of B is B'.
We know that the distance of a point form a line is the length of the perpendicular drawn from the point to the line.
Since HB and HB' are both perpendiculars to EF, so the distance of the vertex B from EF is HB and the distance of the vertex B' from EF is HB'.
Since both B and B' are equidistant from the line EF, so we must have
HB = HB'.
Thus, the correct statement is HB = HB'.
Option (B) is correct.