Question

draw in all lines of symmetry in the shape below. if there are no lines of symmetry, submit an answer without drawing them in. plot a line by clicking in two locations. click a line to delete it.

Explanation:

Step1: Analyze the shape

The given shape is a four - pointed star - like figure made of parallelograms, with a rotational symmetry of order 4. For a figure with rotational symmetry of order \(n\), if \(n\) is even, the number of lines of symmetry is equal to the order of rotational symmetry when the figure is regular in terms of its symmetric parts. Here, we can observe that there are two lines of symmetry that pass through the opposite vertices (or the opposite "points" of the star - like figure) and two lines that pass through the mid - points of the opposite sides (but in this case, due to the shape being made of parallelograms, the lines of symmetry are the ones that bisect the opposite angles or the opposite sides). But more simply, by visual inspection, we can see that there are two lines of symmetry that are perpendicular to each other, passing through the center of the figure. One line goes through the top - bottom "points" and the other goes through the left - right "points".

Step2: Draw the lines of symmetry

We can plot the first line by clicking on two points that lie on the line passing through the top - most vertex and the bottom - most vertex of the figure (passing through the center). Then, we plot the second line by clicking on two points that lie on the line passing through the left - most and right - most vertices (passing through the center).

Answer:

The figure has two lines of symmetry. One line passes through the top and bottom "points" of the star - like figure (through the center), and the other line passes through the left and right "points" of the star - like figure (through the center). To draw them, plot a line connecting the top - most and bottom - most vertices (through the center) and another line connecting the left - most and right - most vertices (through the center).