You can examine them based on their diagonals, their sides or their interior angles. Square – A parallelogram with four congruent sides and four congruent interior anglesįor such simple shapes, parallelograms have some interesting properties. Rectangle – A parallelogram with four congruent interior angles Rhombus (or diamond, rhomb, or lozenge) – A parallelogram with four congruent sides These geometric figures are part of the family of parallelograms: Types of parallelograms Other shapes, however, are types of parallelograms. The name 'parallelogram' gives away one of its identifying properties: two pairs of parallel, opposite sides.Ī parallelogram does not have other names. Another property is that each diagonal forms two congruent triangles inside the parallelogram. One interesting property of a parallelogram is that its two diagonals bisect each other (cut each other in half). In our parallelogram, that means ∠W = ∠Y and ∠X = ∠Z.Ĭonnecting opposite (non-adjacent) vertices gives you diagonals WY and XZ. The interior angles are ∠W, ∠X, ∠Y, and ∠Z. Line segments XY and ZW are also congruent. Notice that line segments WX and YZ are congruent. The four line segments making up the parallelogram are WX, XY, YZ, and ZW. Parallelogram, sides, angles, and diagonals For our parallelogram, we will label it WXYZ, but you can use any four letters as long as they are not the same as each other.

Write a capital letter, then move either clockwise or counterclockwise to the next vertex. Connect the endpoints, and you have a parallelogram! Diagonals of a parallelogram Make sure that second line segment is parallel to (or equidistant from) the first line segment. Use a straightedge (ruler) to draw a horizontal line segment, then draw another identical (congruent) line segment some distance above and to one side of the first one, so they do not line up vertically. Take a rectangle and push either its left or ride side so it leans over you have a parallelogram. So all other quadrilaterals are irregular.Tutors What does a parallelogram look like? The only regular (all sides equal and all angles equal) quadrilateral is a square. and that's it for the special quadrilaterals. one of the diagonals bisects (cuts equally in half) the other.the diagonals, shown as dashed lines above, meet at.The KiteĮach pair is made of two equal-length sides that join up. (the US and UK definitions are swapped over!)Īn Isosceles trapezoid, as shown above, has left and right sides of equal length that join to the base at equal angles. NOTE: Squares, Rectangles and Rhombuses are allĪ trapezoid (called a trapezium in the UK) has a pair of opposite sides parallel.Īnd a trapezium (called a trapezoid in the UK) is a quadrilateral with NO parallel sides: Also opposite anglesĪre equal (angles 'A' are the same, and angles 'B' The ParallelogramĪ parallelogram has opposite sides parallel and equal in length. In other words they 'bisect' (cut in half) each other at right angles.Ī rhombus is sometimes called a rhomb or a diamond.

The RhombusĪ rhombus is a four-sided shape where all sides have equal length (marked 's').Īlso opposite sides are parallel and opposite angles are equal.Īnother interesting thing is that the diagonals (dashed lines) meet in the middle at a right angle. The SquareĪ square has equal sides (marked 's') and every angle is a right angle (90°)Ī square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length). The little squares in each corner mean 'right angle'Ī rectangle is a four-sided shape where every angle is a right angle (90°).Īlso opposite sides are parallel and of equal length. Let us look at each type in turn: The Rectangle Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms. There are special types of quadrilateral: They should add to 360° Types of Quadrilaterals Try drawing a quadrilateral, and measure the angles.

interior angles that add to 360 degrees:.

(Also see this on Interactive Quadrilaterals) Properties

Picture of parallelogram