Related Symmetry
Trapezoids, except for the isosceles trapezoid, do not have any type of symmetry but they are related to symmetry.10 The isosceles trapezoid is the most prevalent trapezoid in elementary school as it is the one in the set of pattern blocks that has two congruent sides. That isosceles trapezoid is half of a regular hexagon. It has three equal sides.
Trapezoids are related to symmetry in the following ways: 1) A trapezoid is half of a parallelogram. A parallelogram does not have a line of symmetry, unless it is a rhombus or a rectangle. A parallelogram has a point of central symmetry. Any line through the central point will cut the parallelogram into two trapezoids, which are congruent under the 180-degree rotation around the central point. (Exception: if the line is a diagonal of the parallelogram, the two halves are triangles.) 2) Triangles are related to parallelograms in a similar way. A triangle is half of a parallelogram in three different ways.11
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