Question

for each figure, identify any lines of symmetry the figure has.

Explanation:

Step1: Recall the definition of line of symmetry

A line of symmetry is a line that divides a figure into two congruent parts such that when the figure is folded along the line, the two parts match exactly.

Step2: Analyze the first figure (Yin - Yang symbol)

If we try to find a line that divides the Yin - Yang symbol into two congruent parts, we see that no such line exists. Because of the small dots (one black and one white) and the shape of the Yin - Yang curves, there is no line of symmetry.

Step3: Analyze the second figure (the cross - like figure)

We can draw a vertical line and a horizontal line through the center of the figure. When we fold the figure along the vertical line, the left and right parts match. When we fold the figure along the horizontal line, the top and bottom parts match. So, it has 2 lines of symmetry (a vertical and a horizontal line through the center of the figure).

Step4: Analyze the third figure (the man - like figure)

If we try to find a line that divides this figure into two congruent parts, we see that no such line exists. The figure is asymmetrical in its current pose.

Answer:

The first figure (Yin - Yang symbol) has no lines of symmetry. The second figure has 2 lines of symmetry (a vertical and a horizontal line through the center of the figure). The third figure has no lines of symmetry.