Question

what types of symmetry does the figure have? explain. the given figure has □ line(s) of reflection and rotational symmetry at □ (type a whole number.)

Explanation:

Step1: Analyze Reflection Symmetry

A square (the figure here, with nested squares and symmetry) has 4 lines of reflection: vertical, horizontal, and two diagonal lines that divide the square into congruent halves.

Step2: Analyze Rotational Symmetry

For rotational symmetry, a square rotated by \(90^\circ\) (\(\frac{360^\circ}{4}\)), \(180^\circ\), \(270^\circ\), and \(360^\circ\) maps onto itself. So the order of rotational symmetry (number of times it maps onto itself during a full rotation) is 4, meaning the angle of rotational symmetry is \(90^\circ\) (since \(\frac{360^\circ}{4} = 90^\circ\)). But the first blank is about lines of reflection, which is 4.

Answer:

4 (for lines of reflection); \(90^\circ\) (for rotational symmetry angle, though the first blank is lines, so 4)

(Note: The first blank asks for lines of reflection, so the answer for that is 4. The second blank for rotational symmetry angle is \(90^\circ\) as the figure (a square - like symmetric figure) has rotational symmetry at \(90^\circ\) intervals.)