Question

analyzing the symmetry of trapezoids
which statements are true regarding the symmetry of the isosceles trapezoid? check all that apply.
the trapezoid has 1 line of reflectional symmetry.
the trapezoid has 2 lines of reflectional symmetry.
the trapezoid has rotational symmetry of order 1.
the trapezoid has rotational symmetry of order 2.
the line of symmetry is a vertical line.

Explanation:

• An isosceles trapezoid has only one line of reflectional symmetry. This line is vertical and passes through the mid - points of the non - parallel sides (the bases).
• Rotational symmetry of order \(n\) means that when the figure is rotated by \(\frac{360^{\circ}}{n}\) about a center point, it maps onto itself. For an isosceles trapezoid, if we rotate it by \(180^{\circ}\) (order \(2\)), it does not map onto itself. Rotational symmetry of order \(1\) means that the only rotation that maps the figure onto itself is \(360^{\circ}\) (which is trivial for any figure).

Answer:

The trapezoid has 1 line of reflectional symmetry. The line of symmetry is a vertical line.