If the quadrilateral has bisecting diagonals, it is a parallelogram You can use proof theorems about a plane, closed quadrilateral to discover if it is a parallelogram: Two pairs of equal and parallel opposite sides Two pairs of congruent (equal), opposite angles You need not go through all four identifying properties.Ĭheck for any one of these identifying properties: Using the properties of diagonals, sides, and angles, you can always identify parallelograms.
This means any two adjacent angles are supplementary (adding to 180°). The two pairs of congruent sides may be, but do not have to be, congruent to each other. The left and right side make a congruent pair. The base and top side make a congruent pair. To be a parallelogram, the base and top sides must be parallel and congruent, and so must the left and right sides. Opposite sides are congruent – The base side ( YZ) and the top side ( WX) of our parallelogram are equal in length (congruent) the left side ( XY) and right side ( ZW) are also congruent The left and right sides ( XY and ZW) are also parallel. The bottom (base) side YZ and top WX are parallel if you were to extend their line segments, they would never meet. Opposite sides are parallel – Look at the parallelogram in our drawing. We already mentioned that their diagonals bisect each other. 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. Tutors What does a parallelogram look like?
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