A parallelogram is a specific type of quadrilateral. In a parallelogram, opposite angles are congruent, opposite sides are congruent, opposite sides are parallel, and the diagonals bisect each other. In the picture above, the window frame is in the shape of a parallelogram.

2. Rhombus

A rhombus is a specific type of quadrilateral and also a specific type of parallelogram. A rhombus has all of the properties of a parallelogram: opposite angles are congruent, opposite sides are congruent, opposite sides are parallel, and diagonals bisect each other. In addition to these four properties, in a rhombus, all sides are congruent, diagonals are perpendicular to one another, and diagonals bisect the opposite angles. In the picture above, the picture of the washcloth is in the shape of a rhombus.

3. Rectangle

A rectangle is a quadrilateral and is a specific parallelogram. A rectangle has all of the properties of a parallelogram: opposite angles are congruent, opposite sides are congruent, opposite sides are parallel, and diagonals bisect each other. In addition to these four properties, the interior angles of a rectangle are congruent, and the diagonals are also congruent. In this picture, the picture frame is in the shape of a rectangle.

4. Square

A square is a quadrilateral and a specific type of parallelogram. A square is a unique figure; it has many distinct properties. A square has all of the properties of a parallelogram: opposite angles are congruent, opposite sides are congruent, opposite sides are parallel, and diagonals bisect each other. In addition to these four properties, a square also has the properties of a rhombus and of a rectangle. Therefore, the additional properties include: all sides are congruent, all angles are congruent, diagonals are perpendicular, diagonals are congruent, diagonals bisect each other, and diagonals bisect opposite angles. In this picture, the clock is in the shape of a square.

5. Trapezoid

A trapezoid is a quadrilateral in which two and only two sides are parallel. The parallel sides of a trapezoid are called the bases and the non-parallel sides are called the legs. The median of a trapezoid is the line segment whose endpoints are the midpoints of the nonparallel sides of the trapezoid. The median is parallel to the bases and the length of the median is equal to one-half the sum of the lengths of the bases. In this image, one side of the popcorn container is a trapezoid.

6. Isosceles Trapezoid

An isosceles trapezoid is a quadrilateral and is also a specific type of trapezoid. An isosceles trapezoid has four sides - two bases and two legs. As in a "regular" trapezoid, the parallel sides of an isosceles trapezoid are the bases and the non-parallel sides are the legs. The median of an isosceles trapezoid is a line segment whose endpoints are the midpoints of the nonparallel sides of the trapezoid and measures one-half of the sum of the bases. The significance of an isosceles trapezoid is that the legs are congruent. In the image above, the platforms used in the gym are stacked and from the side-view, they form an isosceles trapezoid.

My Quadrilaterals Project

1. Parallelogram

A parallelogram is a specific type of quadrilateral. In a parallelogram, opposite angles are congruent, opposite sides are congruent, opposite sides are parallel, and the diagonals bisect each other. In the picture above, the window frame is in the shape of a parallelogram.

2. Rhombus

A rhombus is a specific type of quadrilateral and also a specific type of parallelogram. A rhombus has all of the properties of a parallelogram: opposite angles are congruent, opposite sides are congruent, opposite sides are parallel, and diagonals bisect each other. In addition to these four properties, in a rhombus, all sides are congruent, diagonals are perpendicular to one another, and diagonals bisect the opposite angles. In the picture above, the picture of the washcloth is in the shape of a rhombus.

3. Rectangle

A rectangle is a quadrilateral and is a specific parallelogram. A rectangle has all of the properties of a parallelogram: opposite angles are congruent, opposite sides are congruent, opposite sides are parallel, and diagonals bisect each other. In addition to these four properties, the interior angles of a rectangle are congruent, and the diagonals are also congruent. In this picture, the picture frame is in the shape of a rectangle.

4. Square

A square is a quadrilateral and a specific type of parallelogram. A square is a unique figure; it has many distinct properties. A square has all of the properties of a parallelogram: opposite angles are congruent, opposite sides are congruent, opposite sides are parallel, and diagonals bisect each other. In addition to these four properties, a square also has the properties of a rhombus and of a rectangle. Therefore, the additional properties include: all sides are congruent, all angles are congruent, diagonals are perpendicular, diagonals are congruent, diagonals bisect each other, and diagonals bisect opposite angles. In this picture, the clock is in the shape of a square.

5. Trapezoid

A trapezoid is a quadrilateral in which two and only two sides are parallel. The parallel sides of a trapezoid are called the bases and the non-parallel sides are called the legs. The median of a trapezoid is the line segment whose endpoints are the midpoints of the nonparallel sides of the trapezoid. The median is parallel to the bases and the length of the median is equal to one-half the sum of the lengths of the bases. In this image, one side of the popcorn container is a trapezoid.

6. Isosceles Trapezoid

An isosceles trapezoid is a quadrilateral and is also a specific type of trapezoid. An isosceles trapezoid has four sides - two bases and two legs. As in a "regular" trapezoid, the parallel sides of an isosceles trapezoid are the bases and the non-parallel sides are the legs. The median of an isosceles trapezoid is a line segment whose endpoints are the midpoints of the nonparallel sides of the trapezoid and measures one-half of the sum of the bases. The significance of an isosceles trapezoid is that the legs are congruent. In the image above, the platforms used in the gym are stacked and from the side-view, they form an isosceles trapezoid.

Quadrilaterals Proof