Question

type the correct answer in the box. use numerals instead of words. squares abcd and efgh share a common center on a coordinate plane, as shown in the figure. $overline{eh}$ is parallel to diagonal $overline{ac}$. the number of lines of reflection about which the combined figure can reflect onto itself is .

Explanation:

Step1: Identify square reflection lines

Square ABCD has 4 lines of reflection: its two diagonals ($\overline{AC}$, $\overline{BD}$) and the lines through its midpoints of opposite sides.

Step2: Match inner square symmetry

Square EFGH is rotated so $\overline{EH} \parallel \overline{AC}$. Its reflection lines align exactly with ABCD's 4 lines: reflecting over these lines maps both squares onto themselves, hence the combined figure maps onto itself.

Step3: Count valid reflection lines

All 4 shared reflection lines work for the combined figure.

Answer:

4