Question

symmetry quick check
which of the following summarizes the reflections that carry a parallelogram onto itself? (1 point)
a parallelogram has two lines of reflection that carry it onto itself: one horizontal through the midpoints of each side, and one vertical through the midpoints of the top and bottom.
a parallelogram has two lines of reflection. flipped on each diagonal will carry it onto itself.
a parallelogram has four lines of symmetry: horizontal through the midpoints, vertical through the midpoints, and both diagonals.
a parallelogram does not have any lines of reflection.

Explanation:

Step1: Recall line - symmetry concept

A line of symmetry is a line that divides a figure into two congruent parts such that one part is the mirror - image of the other.

Step2: Analyze parallelogram

For a general parallelogram, no matter which line we try to draw, we cannot divide it into two mirror - image halves. Diagonals of a parallelogram do not act as lines of symmetry as the two triangles formed are not mirror images of each other in the sense of reflection. Also, lines through mid - points of opposite sides do not result in reflection symmetry.

Answer:

D. A parallelogram does not have any lines of reflection