Symmetry and Squares

Hard Geometry And Spatial Sense Symmetry

Consider a square with a line of symmetry that runs diagonally from one vertex to the opposite vertex. If you fold the square along this line, the two halves will match perfectly. Now, if this square contains a smaller square that is positioned at the center and is rotated at an angle of 45 degrees, which of the following choices represents how the smaller square's corners align with the original square's vertices?

The corners of the smaller square touch the midpoints of the sides of the original square.

The corners of the smaller square align with the corners of the original square.

The corners of the smaller square do not touch any part of the original square.

The corners of the smaller square touch the corners of the larger square.

Hint

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