Question

a parallelogram is shown below. line g intersects two vertices. line h bisects each side it passes through. point k is the center of the parallelogram. which transformation(s) must map the parallelogram exactly onto itself? choose all that apply. reflection across line g reflection across line h clockwise rotation about k by 270° counter - clockwise rotation about k by 180° none of the above

Explanation:

Step1: Recall properties of parallelogram

A parallelogram has rotational symmetry of order 2 about its center. A 180 - degree counter - clockwise or clockwise rotation about the center of a parallelogram maps the parallelogram onto itself. A 270 - degree rotation will not map it onto itself.

Step2: Analyze reflections

Line \(h\) bisects the sides of the parallelogram. Reflection across a line that bisects the sides of a parallelogram (like line \(h\)) maps the parallelogram onto itself. Line \(g\) intersects two vertices. Reflection across a line intersecting two vertices of a parallelogram does not map the parallelogram onto itself in general for a non - special parallelogram.

Answer:

Counterclockwise rotation about \(K\) by 180°, Reflection across line \(h\)