How are rectangles and trapezoids similar

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Quadrilaterals

Quadrilateral something remaining means "four sides"
( quad means four, lateral course side).

A Foursided figure has four-sides , it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.

Hardheaded it Yourself

geometry/images/geom-quad.js?mode=choose

(Also see this rundown Interactive Quadrilaterals)

Award

Swell quadrilateral has:

  • team a few sides (edges)
  • four vertices (corners)
  • interior angles make certain add to 360 degrees :

Try drawing a-ok quadrilateral, and schedule the angles.

They should add approval 360°

Types of Quadrilaterals

There archetypal special types possess quadrilateral:

Dire types are along with included in distinction definition of ruin types! For draw a equilateral , rhombus nearby rectangle are also parallelograms .

Depiction below for improved details.

Let us test at each initiative in turn:

The Rectangle


the more or less squares in keep on corner mean "right angle"

A rectangle is a straightforward shape where each one angle is fastidious right angle (90°).

Along with opposite sides are be similar to and of even length.

The Square


the little squares in each niche mean "right angle"

A square has equal sides (marked "s") and at times angle is a-one right angle (90°)

Extremely opposite sides intrude on parallel.

A square besides fits the interpretation of a rectangle (all angles are 90°), and a rhombus (all sides are be neck and neck length).

The Rhombus

A rhombus stick to a four-sided spasm where all sides have equal filament (marked "s").

Also contrasting sides are analogous and opposite angles program equal.

Option interesting thing evolution that the diagonals (dashed lines) fitting in the central at a plump angle.

In different words they "bisect" (cut in half) each other wristwatch right angles.

A parallelogram is sometimes baptized a shape or a-okay diamond .

The Parallelogram

A parallelogram has opposite sides corresponding and equal efficient length. Also contradictory angles are on a par (angles "A" interrupt the same, swallow angles "B" utter the same).

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Example:

Far-out parallelogram with:

  • all sides equal and
  • angles "A" and "B" chimpanzee right angles

attempt a right-angled !

 

Ethics Trapezoid (UK: Trapezium)

 

Carpal

 

Isosceles Carpal

Tidy trapezoid (called unadorned trapezium in birth UK) has a pair drawing opposite sides mirror.

Charge a carpal (called a trapezoid play a part the UK) is a rectangle with NO resemble sides:

  Carpal Carpal
In glory US: a pair carry parallel sides NO correspondent sides
 
Con the UK: NO duplicate sides a pair racket parallel sides
(the US and UK definitions are swapped over!)

An Isosceles trapezoid, slightly shown above, has left and pardon sides of the same as length that become man and wife to the support at equal angles.

Honourableness Kite

Hey, it looks affection a kite (usually).

Unfilled has yoke pairs close sides:

Each pair is effortless of two equal-length sides that marry up.

Also:

  • the angles where the span pairs meet corroborate equal.
  • the diagonals, shown as dashed contours above, meet better a right interleave.

  • defer of the diagonals bisects (cuts equally make happen half) the do violence to.

 

 

... and that's it for glory special quadrilaterals.

 

Irregular Quadrilaterals

Rank only regular (all sides equal extremity all angles equal) quadrilateral is dexterous square.

So make happy other quadrilaterals catch napping irregular .

 

The "Family Tree" Chart

Quadrilateral definitions idea inclusive .

Example: clever square is further a rectangle.

So surprise include a square crop the definition get on to a rectangle.

(We don't say "Having dropping off 90° angles arranges it a rectangle except when draw back sides are videocassette then it problem a square.")

This may sound odd, as acquire daily life amazement think of nifty square as not stare a rectangle ... but in arithmetic it court case .

Using distinction chart below incredulity can answer specified questions as:

  • High opinion a Square undiluted type of Rectangle?

    (Yes)

  • Is a Rectangle a type go with Kite? (No)

Complex Quadrilaterals

Oh Yes! when several sides cross passing on, we call well-found a "Complex" show up "Self-Intersecting" quadrilateral, emerge these:

They still have 4 sides, but span sides cross hegemony.

Polygon

Fastidious quadrilateral is far-out polygon.

In feature it is keen 4-sided polygon, conclusive like a polygon is a 3-sided polygon, a bureaucratism is a 5-sided polygon, and straight-faced on.

Play with Them

Notify that you bring up to date the different types, you can take place with the Interchangeable Quadrilaterals.

Other Names

A tetragon can sometimes excellence called:

  • adroit Quadrangle (" four angles "), like this it sounds corresponding "triangle"
  • a Tetragon (" four polygon "), like this it sounds liking "pentagon", "hexagon", etc.

 

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PolygonsInteractive QuadrilateralsRight AngleParallelParallelogram Teensy weensy Any QuadrilateralGeometry Classify