Quadrilateral Hierarchy by Joseph Bodnar (accelerated reader books TXT) 📕

Quadrilaterals

 

 

 Quadrilateral is the term used to describe any four-sided shape.  The first distinction we make is based upon how many sets of parallel sides it has.  If there are no sets of parallel sides, it is classified as a trapezium.  A quadrilateral with exactly one set of parallel sides is a trapezoid.  When there are two sets of parallel sides, we call it a parallelogram.  Regardless of how many parallel sides there are, the sum of all four angle measurements is 360 degrees in every quadrilateral.

Trapezium

 

A trapezium is a quadrilaterals with no sets of parallel sides.  A trapezium with two sets of congruent adjacent sides is a kite.

 

 

 

The diagonals of a kite are perpendicular.  The longer diagonal bisects the shorter diagonal and bisects the two vertex angles.  The other two angles (called the non-vertex angles) are congruent.

 

Trapezoids

 

 

A trapezoid is a quadrilateral with exactly one set of parallel sides.  The parallel sides are called bases.  Angles that share a base are called base angles. There are two sets of base angles. 

The non-parallel sides might be congruent or not.  If congruent, it called an isosceles trapezoid.  In an isosceles trapezoid, the diagonals are congruent and both sets of base angles are congruent to each other.

 

Parallelograms

 

 

A parallelogram is a quadrilateral with two sets of parallel sides.  Both sets of parallel sides are congruent to each other.  The diagonals of a paralllelogram bisect each other. 

Angles that do not share a side are called opposite angles.  There are two sets of opposite angles.  Both sets of opposite angles are congruent to each other.

Parallelograms can be classified even further based upon the measurements of their sides and angles. 

Rectangles

 

 

 A parallelogram with four right angles is called a rectangle.  The diagonals of a rectangle are congruent.

Rhombi

 

 

A parallelogram with four congruent sides is called a rhombus.  The diagonals of a rhombus are perpendicular.

Squares

 

A parallelogram with four right angles and four congruent sides is a rectobus.  Just kidding; it is a square (a rectobus is what you hope the bus driver doesn't do :) ).

A thing to keep in mind is that all properties of parallelograms apply to rectangles, rhombi and squares, and all properties of rectangles and rhombi apply to squares.  However, the reverse is not true.  Squares have right angles; rhombi may not.  Therefore, all squares are rhombi, but not all rhombi are squares.  Likewise, squares have four congruent sides; rectangles may not.  Thus, all squares are rectangles, but not all rectangles are squares.

 

 

Photo Credits

Cover

Joseph Bodnar.  (2006).  Devil’s Tower.   

 

Page 2

Buscemi, J..  (2010).  Quadrilateral.  [Online image].  

Retrieved without changes (CC BY 2.0) from

https://www.flickr.com/photos/48873600@N08/5294250040/

 

Page 3   

OpenClips.  (2013).  Kite, Autumn, Fall, Wind.

[Online image].  Retrieved under Public Domain CC0 from

http://pixabay.com/en/kite-autumn-fall-wind-146609/

 

Page 5

Vicol, E. R.  Name.  (2010).  

Stanley-Knife-Blades_72959-480x360.  [Online image].

Retrieved without changes (CC BY 2.0) from

https://www.flickr.com/photos/free-stock/4904403661/

 

Page 6   

Raggett, N.  (2006).  

The parallelogram hotel on Long Wharf.  [Online image].

Retrieved without changes (CC BY-ND 2.0) from

https://www.flickr.com/photos/nedraggett/135690444/

 

 

 

Page 7   

Kaser, H.  (2009).  Rectangle.  [Online image].  

Retrieved without changes (CC BY-SA 2.0) from

https://www.flickr.com/photos/hermzz/3764374749/

 

Page 8   

JürnC.  (2011).  File:Borgward-Rhombus.jpg.  

[Online image].  

Retrieved under Creative Commons

Attribution-Share Alike 3.0 Unported from

http://upload.wikimedia.org/wikipedia/commons/7/7e/Borgward-Logo.jpg

 

Page 9   

Ganz, S.  (2007).  Four Square.  [Online image].  

Retrieved without changes (CC BY 2.0) from

https://www.flickr.com/photos/steveganz/392503377/

Imprint

Publication Date: 04-14-2014

All Rights Reserved