Quadrilaterals
copyright 2011 by Tim Griffin

Teacher said I have to learn my quadrilaterals now
I said I’d like to help you ma’am but I really don’t know how
She said I only have to look at the angles and the lines
Cause that’s how quadrilaterals are defined

(chorus) A trapezoid got a pair of parallel sides and a parallelogram got two
A rhombus got four equal sides, I’ll count them out for you
Squares and rectangles got right angles like a window or a door
But I don’t know what a quadrilateral’s for, one two three four!

A quadrilateral’s any polygon that’s got four sides
To find the area just multiply how high it is by how wide
To get perimeter simply measure the sides and find the sum
And here’s the part where the definitions come

(repeat chorus)

Squares and rectangles are defined by perpendicular lines
The square’s got the stricter definition: it’s got four equal sides
So a square is a rhombus and a parallelogram and a rectangle to boot
Its angles are neither obtuse nor acute

(repeat chorus)

A quadrilateral’s got four angles for 360 degrees
You can add three angles and subtract from 360 to get a missing angle with ease
So just remember the sides and the angles are your most important tools
And any quad that’s not scalene will follow these rules:

(repeat chorus)

Notes

At its most basic level, geometry is largely about some highly specialized definitions: what exactly is the difference between a rhombus and a trapezoid, you say? Well, here you go. Naturally, we sing a song about quadrilaterals in 4/4 time with four chords.

Here are some standards from the Common Core and the state of California addressed by this song:

Second Grade:

• CA.M2.MG.2.1 Describe and classify plane and solid geometric shapes (e.g., circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices.

Third Grade:

• Math 3.G.1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
• CA.M3.MG.1.3 Find the perimeter of a polygon with integer sides.
• CA.M3.MG.2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).

Fourth Grade:

• Math 4.G.2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size.
• CA.M4.MG.1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.
• CA.M4.MG.3.5 Know the definitions of a right angle, an acute angle, and an obtuse angle. Under­ stand that 90°, 180°, 270°, and 360° are associated, respectively, with 1⁄4, 1⁄2, 3⁄4, and full turns.

Fifth Grade:

• Math 5.G.3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Math 5.G.4. Classify two-dimensional figures in a hierarchy based on properties.
• CA.M5.MG.1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram).

Sixth Grade:

• Math 6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Guitar Chords:
E, G, A, B