## Rhombus Definition

A rhombus is a quadrilateral (plane figure, closed shape, 4 sides) with 4 equal-length sides and also opposite political parties parallel to every other. Every rhombuses space parallelograms, however not all parallelograms space rhombuses. Every squares are rhombuses, but not every rhombuses space squares. The opposite inner angles that rhombuses space congruent. Diagonals of a rhombus always bisect each various other at ideal angles.

You are watching: Are the diagonals of a rhombus always congruent ## How To build a Rhombus

You can construct a rhombus best now, on any kind of flat surface, if you have 4 identical, linear objects. Toothpicks, pencils, meter rod -- any type of four congruent, right line segments will do.

Lay the four straight objects the end on the flat surface so their eight end touch in only four places. You can not fail at this! Lay 2 objects down to it is in parallel to every other yet a slight street apart. If you usage the various other two objects to attach end points, you have a rhombus!

## What walk a Rhombus look at like?

The opposite sides of her quadrilateral will be parallel, and also opposite angles will certainly be the very same (congruent). Her quadrilateral by an interpretation must it is in a rhombus! ## Is a Square a Rhombus?

If you have actually a rhombus with 4 equal internal angles, you have actually a square. A square is a special situation of a rhombus, due to the fact that it has four equal-length sides and also goes over and beyond that to also have four right angles.

## Rhombus Shape

Most times, the rhombus you see will be drawn so it has a basic -- 2 opposite sides will be horizontal, with the bottom next serving as the shape"s base. Be careful, though, because a rhombus can appear at any kind of orientation. When it "stands up" so the is symmetrical in appearance, (its diagonals room horizontal and also vertical) it is usually called a diamond.

If you struggle to mental its name, think the a square that has actually been run into by a bus, so the is tilted over (run into by a bus … rhombus).

## Properties that a Rhombus

One of the two qualities that make a rhombus distinct is the its 4 sides room equal in length, or congruent. The various other identifying home is that opposite sides space parallel.

If you have a quadrilateral with just one pair of parallel sides, you definitely do not have a rhombus (because 2 of its political parties cannot be the exact same length). You have actually a trapezoid.

If you have a quadrilateral through two bag of parallel sides, you do not necessarily have actually a rhombus; you could have a parallelogram, or you can have a rhombus if all four sides space the very same length. ## Rhombus Angles

In enhancement to those four sides, the rhombus has 4 interior angles. Girlfriend can additionally construct 2 diagonals inside the rhombus by connecting the contrary vertices (corners). No matter just how you arrange those 4 linear objects top top your flat surface, friend will constantly have 2 pairs of equal opposite angles. Start over v two of your objects and also this time, concentration on do an acute (less than 90°) angle out of them. Use the various other two objects to attach the original two, up and also to the right, come make your four-sided (quadrilateral), airplane figure --a rhombus.

Look at the bottom left angle and the optimal right angle. They space the same. They are congruent. Look in ~ the bottom best angle and the top left angle: they room congruent. Opposite inner angles that a rhombus are congruent.

## Diagonals the a Rhombus

A wonderful and rare building of a rhombus is that its diagonals are always perpendicular to each other. You have the right to see this for yourself if friend lay down your four straight objects to make a rhombus and then draw in diagonals. No matter what angle you have actually for the rhombus"s 4 vertices, the diagonals the a rhombus are always at best angles to every other. These diagonals likewise cut every other exactly in half. Geometricians say they bisect every other. That means the 2 diagonals division the rhombus up into 4 right-angle triangles.

## Lesson Summary

A rhombus is a quadrilateral (plane figure, close up door shape, 4 sides) with 4 equal-length sides and opposite sides parallel to each other. Every rhombuses space parallelograms, however not all parallelograms space rhombuses. Every squares room rhombuses, yet not every rhombuses are squares. The opposite interior angles of rhombuses room congruent. Diagonals that a rhombus always bisect each other at best angles.

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## What friend learned:

Once you watch this lesson and read about a rhombus, you will know just how this plane figure fits into the totality family of airplane figures, what properties do a rhombus unique, and how to recognize a rhombus by recognize its two special identifying properties.