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:

• Line of reflectional symmetry: An isosceles trapezoid has only 1 line of reflectional symmetry. This line passes through the mid - points of the non - parallel sides (the legs) and is vertical (assuming the bases are horizontal).
• Rotational symmetry: For rotational symmetry, a figure has rotational symmetry of order \(n\) if it looks the same after a rotation of \(\frac{360^{\circ}}{n}\). An isosceles trapezoid does not look the same after a rotation of \(180^{\circ}\) (so order 2 is out). A rotation of \(360^{\circ}\) (order 1) is trivial for any non - moving object.

Answer:

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