In addition to being four-sided polygons, all quadrilaterals share some additional properties. This may be accessible for middle grade students who have learned about perpendicular lines and bisectors. Given 6 toy horses and 4 toy cows, and asked whether there are more horses or more animals, very young children often answer “more horses” because in classifying the toys as “horses,” they, for that moment, exclude them as “animals,” even though, if separately asked whether horses are animals, they will say yes.Īnother possible way to classify quadrilaterals is by examining their diagonals.Similarly, students tend to treat rectangles and parallelograms as disjoint classes, rather than seeing a rectangle as a special type of parallelograms. Casual language also treats shape-names as “exclusive” rather than “inclusive.” Thus, casual language treats square and rectangle as distinct, rather than treating square as a special kind of rectangle, as mathematics does. In the classification scheme below, rectangles ( F and B) have the right hand column to themselves, but parallelograms are not grouped in a way that excludes A, which is not a parallelogram.Ĭhildren in primary grades often find it hard to assign anything (geometrical or otherwise) simultaneously to two categories. In the classification scheme shown above, parallelograms ( B, C, D, E, and F) have a place of their own (the right hand column), and even rhombuses ( B, C, D) have a place (the bottom row), but rectangles ( F and B) aren’t distinguished from the others. Though the names that are given to individual figures does not change, the way that they are grouped may depend on the characteristics used to sort them. The square is also the name of the regular quadrilateral - one in which all sides are congruent and all angles are congruent. squares ( B), the most special of them all and sometimes.Elementary school typically has children learn the names of The names of many of these special quadrilaterals are also typically part of the elementary curriculum, though little else about the properties of these figures may be studied until high school. The classification schemes taught in elementary school involve the number of pairs of parallel sides, and the congruence of sides, and whether or not all the angles are right angles (all angles are congruent).
Quadrilaterals can be classified by whether or not their sides, angles, diagonals, or vertices have special properties.
Like all polygons that have more than three sides, quadrilaterals can be convex like these, ,, or concave like these. Just as triangles and quadrilaterals are special types of polygons, there are many subclasses of quadrilaterals. Lateral means “side” (think of football, for example). Quadri- (four) + -lateral (side) means “four-sided.”Ĭompare quadri- to Spanish cuatro. squares ( B), the most special of them all.rhombuses ( C and D are the “typical” examples, but all squares also fit the definition of rhombuses).rectangles ( F is the “typical” example, but all squares also fit the definition of rectangles).parallelograms ( E is the “typical” example, but all rectangles and rhombuses also fit the definition of parallelograms).trapezoids ( A and J are “typical” examples, but all parallelograms also fit the definition of trapezoids).See the articles on each type for their definitions and special properties. Most of the time, context will make clear what you mean, but you should remain aware that in some cases you may need to clarify.Įlementary school curricula typically have children learn the names of special subsets of quadrilaterals with particular features. The usual definitions of polygons, however, refer only to the line segments that form the edges of the polygon. When we talk about “dissecting” a parallelogram and rearranging the parts to form a rectangle in order to determine the area of the parallelogram, we are clearly referring to the edges and the interior. (This also means that a quadrilateral has exactly four vertices, and exactly four angles.)ĭiscussions of 2-D shapes sometimes refer only to the boundary (the line segments that form the edges of the figure) or to the interior as well. (This also means that a quadrilateral has exactly four vertices, and exactly four angles.) MeaningĪ quadrilateral is a polygon that has exactly four sides.
A quadrilateral is a polygon that has exactly four sides.
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