# Relationship between parallelograms and trapezoids

### Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram

A Venn diagram uses overlapping circles to show relationships between groups into three sub-groups: general quadrilaterals, parallelograms and trapezoids. In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred 12 See also; 13 References; 14 Further reading; 15 External links A parallelogram is a trapezoid with two pairs of parallel sides. the same ratio (this ratio is the same as that between the lengths of the parallel sides). A trapezoid has one pair of parallel sides and a parallelogram has two pairs of The inclusive definition sets up a relationship between parallelograms and.

Under the inclusive definition, all parallelograms including rhombusesrectangles and squares are trapezoids. Rectangles have mirror symmetry on mid-edges; rhombuses have mirror symmetry on vertices, while squares have mirror symmetry on both mid-edges and vertices.

Special cases[ edit ] Trapezoid special cases. The orange figures also qualify as parallelograms. A right trapezoid also called right-angled trapezoid has two adjacent right angles.

### Trapezoid - Wikipedia

An acute trapezoid has two adjacent acute angles on its longer base edge, while an obtuse trapezoid has one acute and one obtuse angle on each base. An isosceles trapezoid is a trapezoid where the sides legs have the same length, and the base angles have the same measure. It has reflection symmetry. This is possible for acute or right trapezoids. A parallelogram is a trapezoid with two pairs of parallel sides.

**What Is the Difference Between a Trapezoid & a Parallelogram? : Math Instruction**

A parallelogram has central 2-fold rotational symmetry or point reflection symmetry. Properties At least one pair of opposite sides are parallel.

Angles between pairs of parallel sides are supplementary. The parallel sides are the bases.

The non-parallel sides are the legs. It has two pair of base angles.

Properties of an isosceles trapezoid a special type of trapezoid. The properties of trapezoid apply by definition parallel bases. The legs are congruent by definition.

The lower base angles are congruent.

## What is a Trapezoid? (Part 2)

The upper base angles are congruent. Any lower base angle is supplementary to any upper base angle. The diagonals are congruent.

Diagonals of a parallelogram bisect each other, Opposite sides of a parallelogram are parallel by definition and so will never intersect. The area of a parallelogram is twice the area of a triangle created by one of its diagonals. The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides. Any line through the midpoint of a parallelogram bisects the area.