, 2020

For $BD$ to be a line of symmetry of $ABCD$, the squares labelled $P$ and $S$ should be shaded. [[IMAGE0]] To see why this is, consider that the reflection in $BD$ of vertex $A$ is vertex $C$, and so the reflection in $BD$ of side $DA$ is side $DC$. Further, the reflection in $BD$ of the first column of square $ABCD$ is the first row of square $ABCD$. Thus, the reflection in $BD$ of the shaded square in row 3, column 1 is the square in row 1, column 3 (the square labelled $P$). More generally, the reflection in $BD$ of the square in row $r$, column $c$ is the square in row $c$, column $r$. Thus, the reflection in $BD$ of the shaded square in row 5, column 2 is the square in row 2, column 5 (the square labelled $S$).