Question

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:

Step1: Analyze reflectional symmetry

An isosceles trapezoid has only 1 line of reflectional symmetry. This line is the vertical line that passes through the mid - points of the non - parallel sides (the bases). So, the statement "The trapezoid has 1 line of reflectional symmetry" is true and "The trapezoid has 2 lines of reflectional symmetry" is false.

Step2: Analyze 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 looks the same only after a rotation of \(360^{\circ}\) (since rotating it by any other angle less than \(360^{\circ}\) will not map it onto itself). Since \(\frac{360^{\circ}}{1}=360^{\circ}\), the trapezoid has rotational symmetry of order 1. So, the statement "The trapezoid has rotational symmetry of order 1" is true and "The trapezoid has rotational symmetry of order 2" is false.

Step3: Determine the line of symmetry

By the definition of an isosceles trapezoid and its reflectional symmetry, the line of symmetry is a vertical line (passing through the mid - points of the non - parallel sides). So, the statement "The line of symmetry is a vertical line" is true.

Answer:

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