Askjagden's Guide to Geometry: Quadrilaterals

Askjagden's Guide to Geometry: Quadrilaterals

What are quadrilaterals? Quadrilaterals are polygons with four angles and sides. Quadrilaterals have a sum total of 360 degrees for exterior and interior angles. You can prove this by plugging and slugging: (4 - 2)(180) = 2(180) = 360.

There are multiple types of quadrilaterals. One is the parallelogram. It pertains to its name. The opposite sides of the parallelogram are parallel and congruent. To find the area of the quadrilateral, you must multiple the base by the height. Another characteristic of parallelograms is that their diagonals bisect each other. The three types of parallelograms are squares, rectangles, and rhombuses. Squares are regular parallelograms. Rectangles are equilangular parallelograms. Rhombuses are equilateral parallelograms. Squares are rectangles and rhombuses, but rectangles and rhombuses are not squares.

Another quadrilateral is the kite. A kite has two pairs of consecutively congruent sides, but the opposite sides are not congruent. The areas of kites and rhombuses can be found my multiplying the first diagonal by the second diagonal and then dividing by 2, or d_1(d_2)(1/2).

Have fun with geometry!