Classify Shapes in a Hierarchy (Quadrilaterals & Triangles)

It tells you the size of the turn, or amount or rotation between the two adjacent lines, rays, or line segments.

It means that one side of the shape is a mirror image of the other.

The tracks are parallel because they continue on without ever getting closer to one another, or farther apart.

The railway ties are perpendicular to the tracks because they cross at a 90° angle.

A closed shape has all of the edges connecting at endpoints, so there are no gaps in the perimeter (distance around the outside of a shape). A closed shape has area.

It means that a parallelogram has all the properties of a quadrilateral, plus the properties specific to parallelograms.

The square inherits the properties of the kite (two sets of adjacent sides with equal length) through the rhombus (four equal sides), and the properties of the parallelogram (two sets of parallel sides) through the rectangle (all right angles). Because the square keeps the properties that define its supergroups, a square is also a parallelogram and a kite.

No. A triangle and a quadrilateral are both classified on the property of “number of sides.” A triangle is a shape with exactly three sides, and a quadrilateral is a shape with exactly four sides. This means that a shape cannot be both a triangle and a quadrilateral.

(Exclusive definition) No. A trapezoid is a shape with exactly one set of parallel sides, so a parallelogram cannot be a trapezoid. (Inclusive definition) Yes. A trapezoid is a shape with at least one set of parallel sides, so parallelogram is a subgroup of trapezoid.

A hierarchy is a system of classification based on sets of properties that become more and more specific as you move down the hierarchy. All subgroups retain all the properties of their supergroups, so in geometry, shapes inherit the properties of the categories above them in the hierarchy.