for a shape to be called a rhombus what must it have
Table of Contents
- Rhombus Definition
- How To Construct a Rhomb
- What does a Rhombus look similar?
- Dissimilar Names For A Rhomb
- Is a Square a Rhombus?
- Rhombus Shape
- Backdrop of a Rhombus
- Rhombus Angles
- Diagonals of a Rhombus
Rhomb Definition
A rhombus is a quadrilateral (plane figure, closed shape, four sides) with four equal-length sides and reverse sides parallel to each other. All rhombuses are parallelograms, but not all parallelograms are rhombuses. All squares are rhombuses, just not all rhombuses are squares. The opposite interior angles of rhombuses are congruent. Diagonals of a rhombus always bisect each other at right angles.
How To Construct a Rhombus
You can build a rhombus right now, on any flat surface, if you have four identical, linear objects. Toothpicks, pencils, meter sticks -- whatever four coinciding, straight line segments volition exercise.
Lay the four straight objects out on the flat surface so their viii ends touch in only four places. You cannot fail at this! Lay ii objects down to be parallel to each other just a slight distance apart. If you apply the other 2 objects to connect cease points, you accept a rhombus!
What does a Rhombus look like?
The contrary sides of your quadrilateral volition exist parallel, and opposite angles will be the same (congruent). Your quadrilateral by definition must be a rhombus!
This ways every rhombus is:
Different Names For A Rhomb
A rhombus can have three additional names:
- Rhomb
- Lozenge
- Diamond
A rhombus is a special case of a parallelogram, considering it fulfills the requirements of a parallelogram: a quadrilateral with two pairs of parallel sides. Information technology goes above and beyond that to likewise have four equal-length sides, but it is still a type of parallelogram.
Every rhombus you see volition too be a parallelogram, but not every parallelogram you come across will be a rhombus.
Is a Square a Rhombus?
If you take a rhombus with four equal interior angles, you have a square. A square is a special case of a rhombus, because it has four equal-length sides and goes above and beyond that to also accept four correct angles.
Every foursquare you lot see will be a rhombus, but non every rhombus you meet will be a square.
Rhombus Shape
About times, the rhombus yous see will exist drawn so it has a base -- two opposite sides volition exist horizontal, with the bottom side serving equally the shape's base.
Be careful, though, because a rhomb can appear at whatever orientation. When it "stands up" so it is symmetrical in appearance, (its diagonals are horizontal and vertical) it is usually chosen a diamond.
If you struggle to call up its proper noun, retrieve of a square that has been run into by a bus, so it is tilted over (run into past a bus … rhombus).
Properties of a Rhombus
1 of the two characteristics that brand a rhombus unique is that its four sides are equal in length, or coinciding. The other identifying property is that contrary sides are parallel.
If you take a quadrilateral with merely one pair of parallel sides, you definitely practise not have a rhombus (considering two of its sides cannot be the same length). Y'all have a trapezoid.
If you lot accept a quadrilateral with two pairs of parallel sides, y'all do not necessarily have a rhombus; y'all might have a parallelogram, or you could accept a rhombus if all 4 sides are the aforementioned length.
Rhombus Angles
In addition to those four sides, the rhombus has four interior angles. You can likewise construct ii diagonals inside the rhomb by connecting reverse vertices (corners).
No matter how y'all suit those four linear objects on your flat surface, y'all will ever accept ii pairs of equal contrary angles. Outset over with two of your objects and this time, concentrate on making an acute (less than 90°) angle out of them. Use the other ii objects to connect the original 2, up and to the correct, to make your four-sided (quadrilateral), airplane figure --a rhombus.
Look at the lesser left bending and the peak correct angle. They are the same. They are coinciding. Await at the lesser right angle and the tiptop left angle: they are coinciding. Opposite interior angles of a rhombus are coinciding.
The 4 interior angles of a rhombus always add together up to 360°.
Diagonals of a Rhomb
A wonderful and rare property of a rhombus is that its diagonals are e'er perpendicular to each other. You can see this for yourself if you lay downwards your four straight objects to make a rhombus and so draw in diagonals. No matter what angles y'all accept for the rhombus's 4 vertices, the diagonals of a rhombus are always at right angles to each other.
These diagonals also cutting each other exactly in half. Geometricians say they bisect each other. That means the two diagonals dissever the rhomb upwardly into four right-angle triangles.
Lesson Summary
A rhomb is a quadrilateral (plane effigy, airtight shape, four sides) with 4 equal-length sides and opposite sides parallel to each other. All rhombuses are parallelograms, simply not all parallelograms are rhombuses. All squares are rhombuses, but not all rhombuses are squares. The reverse interior angles of rhombuses are congruent. Diagonals of a rhombus always bisect each other at right angles.
What you learned:
In one case yous spotter this lesson and read nearly a rhombus, you lot will know how this plane effigy fits into the whole family of plane figures, what properties brand a rhombus unique, and how to recognize a rhombus by finding its two special identifying properties.
Adjacent Lesson:
How To Find the Surface area of a Rhombus
Source: https://tutors.com/math-tutors/geometry-help/what-is-a-rhombus-definition-properties
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