True or False: If a figure does not have point symmetry, it cannot have reflection symmetry.
false
True. If a figure does not have point symmetry, it cannot have reflection symmetry. Point symmetry, also known as rotational symmetry, is the property of a figure to be unchanged by rotation around a fixed point. Reflection symmetry, also known as line symmetry, is the property of a figure to be unchanged by reflection over a line.
To determine if a figure has point symmetry, you can look for a point around which the figure can be rotated by a certain angle and still appear the same. If such a point exists, the figure has point symmetry. On the other hand, to determine if a figure has reflection symmetry, you can check if there is a line that divides the figure into two equal halves, such that each half is a mirror image of the other.
If a figure does not possess point symmetry, it means that there is no point around which the figure can be rotated to appear the same. In this case, it is not possible for the figure to have reflection symmetry as well, since reflection symmetry can be thought of as a special case of point symmetry where the rotation angle is exactly 180 degrees.