Question

analyzing the symmetry of trapezoids
w z
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
x y

Explanation:

• Reflexional symmetry:
• An isosceles trapezoid has only 1 line of reflexional symmetry. This line passes through the mid - points of the non - parallel sides (the legs) and is a vertical line (assuming the trapezoid is oriented with the bases horizontal). So, the statement "The trapezoid has 1 line of reflexional symmetry" is true and "The trapezoid has 2 lines of reflexional symmetry" is false.
• Rotational symmetry:
• For rotational symmetry, a shape has rotational symmetry of order \(n\) if when rotated by \(\frac{360^{\circ}}{n}\) about a center point, it maps onto itself. An isosceles trapezoid does not map onto itself when rotated by \(180^{\circ}\) (order 2). In fact, the only rotation that maps it onto itself is a \(360^{\circ}\) rotation (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.
• Line of symmetry orientation:
• Since the non - parallel sides (legs) are congruent and the bases are parallel, the line of symmetry is vertical (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 reflexional symmetry.
• The trapezoid has rotational symmetry of order 1.
• The line of symmetry is a vertical line.