**Quadrilateral Family Tree**

Kite:

Trapezoid

Right:

Isosceles:

Trapezoid:

Parallelogram:

Rhombus:

Rectangle:

Square:

Irregular:

Convex:

Table of Contents

Kite

Trapezoid

-Right

-Isosceles

Parallelogram

-Rhombus

-Rectangle

--Square

Irregular Concave

**Katie Hill**

**April 18, 2013**

A quadrilateral with exactly two pairs of congruent consecutive sides.

A quadrilateral with exactly one pair of parallel lines.

A trapezoid with exactly two right angles.

A trapezoid with two congruent legs, congruent base angles and upper base angles.

A quadrilateral with two pairs of parallel sides.

A parallelogram with four congruent sides.

A parallelogram with four right angles.

A quadrilateral that does not have all four angles and sides congruent.

An irregular quadrilateral in which no diagonal contains points in the exterior of the polygon.

A rectangle with four congruent sides.

Light switches have four right angles, making them rectangles. Light switch frames with only one switch are rectangles because the right angles allow the shape to be cut out with less waste than other shapes.

In white boards, the opposite lines are parallel. They are rectangles because rectangles' parallel sides fit together on the wall without gaps or wasted space.

Exit signs are rectangles because they have four right angles. The rectangle shape is easy for the eyes to scan over and quickly extrapolate the message, so when people are in a hurry their brains don't waste time interpreting data about shapes and read the message with fewer distractions.

Recycling bins in the hallway have two sides of equal length that taper at the base. Isosceles trapezoids have a smaller surface area than rectangles of the same dimensions, so these bins use less material.

The arms of chairs and couches in the room by the counselor's office get wider where the hand lies at the end of the chair, for practical reasons.

The chair and couch legs in the school are trapezoidal because it has one pair of parallel lines. The chair legs need to have parallel sides on which the chair can balance.

Pie servers in the kitchen have

tapering sides to reflect the shape of pie slices. Like when dividing polygons at the vertexes, dividing circular pies creates triangles (with one rounded side) that taper to a point ending at the centroid.

Roof ridges on the entryway of the Science and Engineering building have one pair of parallel lines. They allow rain water to flow off the roof in sections, not a sheet. They help with drainage and aesthetics.

Students' laptops have two congruent sides. Modern laptops are trapezoids because they use less material than rectangles, making them lighter and cheaper to produce.

The recycle sign on recycling bins has right angles, and is cut off at the top by a folded look of the arrow. The arrow would be a rectangle if it were not folded to signify recycling.

This railing support in the stairway has one set of parallel lines to distribute weight evenly.

The trapezoid at the base of the entrance stairway would usually be a rectangle so the walls fit together easily, but the stairway cut through it.

This control box for the printer

in the commons has two right angles, and the top side is sloping down to improve viability of the controls.

The glass wall bricks found in the science and engineering building have two sets of parallel lines so the bricks fit together tightly with no gaps that allow air through.

The railing of the staircase in the science and engineering has numerous parallel lines because the stairs are on an incline, and all of the rods run parallel to the staircase and therefore themselves.

Some lead containers, found in supply bags, are parallelograms. Obtuse angles and the supplementary acute angles create a semi flat irregular shape that does not fit together with the pencils in the supply bag, so it is easy to extract.

Because rhombuses have four congruent sides, they can fit together in aesthetically pleasing patterns. The background on a student's phone shows that the sum of the obtuse angle of three congruent rhombuses is 360 degrees, and the exterior sides create a hexagon.

Students enjoy stimulating their

minds with rubix cubes at school. Some of them have rubix cubes in irregular shapes, like rhombuses or even pentagons. All four sides of this rubix cube are the same length so it remains the same shape when it is scrambles, without pieces with exposed edges.

Fabric designs often utilize rhombuses four congruent side lengths in the pattern found on a pillow. When the acute angles of eight congruent rhombuses share a vertex, their sum in 360 degrees, creating an aesthetically pleasing design.

Kite shaped die, used for games and probability, have two sets of congruent adjacent lines. If a midsegment were to divide the kite shaped die from the vertex shared by the longer lines to the vertex shared by the shorter lines, the two sides would be equal. When it is spun on the vertex where the larger set of adjacent lines meet, there is an equal chance that the die lands on any side.

Kite shaped charms on jewelry can be kites because kites are aesthetically pleasing. There is a line of symmetry running from the vertex shared by the longer lines to the vertex shared by the shorter lines, so both halves of the shapes are equal in size, and if created properly, weight. This way the charm hangs straight down and does not lean to any one side.

Kites are kite shaped because the vertex of the shorter congruent adjacent line pair can cut through the wind better than the vertex of a rectangle, as the kite's vertex's angle is less than 90 degrees, and smaller angles are better for cutting into the wind. Also, the diagonals bisect, which gives the kite its strength. The kite is more aerodynamic and easier to fly.

Stair/exit sides in stairways have four congruent sides to make them simple and plain and regular. The top and bottom lines are parallel to the ceiling and floor, and perpendicular to the edges of the wall they are placed on. Their purpose is to be a label, a sign, not to catch eyes.

The fire alarms scattered around the building have four right angles and four congruent sides. It doesn't take up very much space, and the square shape, paired with bright red paint and a large flashing light, are easy to spot and the message it carries is obvious: fire.

Power outlet covers with four outlets have four right angles and four congruent sides are space and material efficient.

The entry code box beside the door at the Science and Engineering building is an irregular shape because it is not regular, like a square. The top side is slanted up for better visibility, and the bottom side slants down so rain water will follow it and slide down the wall instead of dripping off the edge of the box.

Lunch trays in the cafeteria have four right angles. They are related to regular squares in that way, but rectangles have two sets of congruent lines while squares have four congruent sides. Lunch trays are rectangles because they fit together well to preserve space and are easy to store between lunches.

The wet floor sign next to the water fountain does not have four right angles, so it is not a regular shape. The trapezoidal shape uses less material.