7.4: Quadrilaterals

A quadrilateral can be considered ANY four sided figure. The sides and angles don't need to be congruent or have any certain pattern.

A quadrilateral is the GENERAL NAME for any four sided figure.

Parallelograms are a specific "family" in the quadrilaterals where the opposite sides (top/bottom and left/right) are parallel to each other AND are congruent.

The rectangle is part of the parallelogram family because its opposite sides are parallel and congruent.

However, in rectangles, there also need to be four right angles.

The rhombus is part of the parallelogram family because its opposite sides are parallel and congruent.

However, in rhombi (the plural for a rhombus), the four sides are ALL congruent.

The square is part of the parallelogram family because its opposite sides are parallel and congruent.

However, squares inherit the properties of BOTH the rectangle and rhombus. So, squares not only have the properties of parallelograms, but have four right angles and four congruent sides.

A trapezoid is NOT part of the parallelogram family. Instead of having two pairs of parallel sides, the trapezoid will only have ONE pair of parallel sides.

The kite is a NOT a parallelogram or a trapezoid, but is its own quadrilateral. In a kite, there are two pairs of adjacent sides that are congruent (in this example, the sides meeting at a vertex on the left are congruent and the same for the sides that meet at a vertex on the right.

Words: The sum of the angle measures of a quadrilateral is 360°.

Algebra: w + x + y + z = 360