# Is a rhombus a quadrilateral

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## Quadrilaterals Properties | Parallelograms, Trapezium, Rhombus How to Prove That a Quadrilateral Is a Parallelogram With Diagonals : Parallelograms & Math

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Prove that when in a rectangle, the midpoints of the sides of the rectangle are drawn and labeled A , B , C , and D , then the quadrilateral A B C D is a rhombus. Say that the rectangle had side lengths of length e and f. Since all sides of this quadrilateral are equal then quadrilateral A B C D must be a rhombus. Geometry Quadrilaterals: Rhombi Proving a Quadrilateral Is a Rhombus To prove a quadrilateral is a rhombus, here are three approaches: 1 Show that the shape is a parallelogram with equal length sides; 2 Show that the shape's diagonals are each others' perpendicular bisectors; or 3 Show that the shape's diagonals bisect both pairs of opposite angles. Proving a Quadrilateral Is a Rhombus. Explanations 1.

Quadrilateral just means "four sides" quad means four, lateral means side. A Quadrilateral has four-sides , it is 2-dimensional a flat shape , closed the lines join up , and has straight sides. Also see this on Interactive Quadrilaterals. Try drawing a quadrilateral, and measure the angles. Some types are also included in the definition of other types! For example a square , rhombus and rectangle are also parallelograms.

There are many different kinds of quadrilaterals, but all have several things in common: all of them have four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals degrees. This is how they are alike, but what makes them different? We know many quadrilaterals by their special shapes and properties, like squares. Remember, if you see the word quadrilateral, it does not necessarily mean a figure with special properties like a square or rectangle! In word problems, be careful not to assume that a quadrilateral has parallel sides or equal sides unless that is stated.

In plane Euclidean geometry , a rhombus plural rhombi or rhombuses is a simple non-self-intersecting quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral , since equilateral means that all of its sides are equal in length. Every rhombus is a parallelogram and a kite. A rhombus with right angles is a square. The surface we refer to as rhombus today is a cross section of this solid rhombus through the apex of each of the two cones.

Do opposite sides in a quadrilateral have to be equal in order for it to have diagonals that are perpendicular? It is not correct. The diagonals are perpendicular if and only if all the sides are equal as in the case of a rhombus or a square. The diagonals will be perpendicular also if the pairs of adjacent sides are equal as in the case of a kite. No they are not.

A quadrilateral is a polygon with four sides. There are seven quadrilaterals, some that are surely familiar to you, and some that may not be so familiar. Check out the following definitions and the quadrilateral family tree in the following figure. If you know what the quadrilaterals look like, their definitions should make sense and be pretty easy to understand though the kite definition is a bit of a mouthful. Here are the seven quadrilaterals:.

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## Quadrilaterals: Classification

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## 1 thoughts on “Is a rhombus a quadrilateral”

1. Matt T. on said:

A quadrilateral is a polygon with four sides.