6.8. Quadrilateral Classification http://www.ck12.org
If it turns out that your guess was wrong because the shape does not fulfill the necessary properties, you can guess
again. If it appears to be no type of special quadrilateral then it is simply a quadrilateral
The examples below will help you to see what this process might look like.
Example A
Determine what type of parallelogramT U NEis:T( 0 , 10 ),U( 4 , 2 ),N(− 2 ,− 1 ), andE(− 6 , 7 ).
This looksT U NEis a rectangle.
EU=
√
(− 6 − 4 )^2 +( 7 − 2 )^2 T N=
√
( 0 + 2 )^2 +( 10 + 1 )^2
=
√
(− 10 )^2 + 52 =
√
22 + 112
=
√
100 + 25 =
√
4 + 121
=
√
125 =
√
125
If the diagonals are also perpendicular, thenT U NEis a square.
Slope ofEU=−^76 −−^24 =− 105 =−^12 Slope ofT N=^100 −−((−− 21 ))=^112
The slope ofEU 6 =slope ofT N, soT U NEis a rectangle.
Example B
A quadrilateral is defined by the four linesy= 2 x+1,y=−x+5,y= 2 x−4, andy=−x−5. Is this quadrilateral
a parallelogram?
To check if its a parallelogram we have to check that it has two pairs of parallel sides. From the equations we can
see that the slopes of the lines are 2,−1, 2 and−1. Because two pairs of slopes match, this shape has two pairs of
parallel sides and is a parallelogram.
Example C
Determine what type of quadrilateralRST Vis. Simplify all radicals.
There are two directions you could take here. First, you could determine if the diagonals bisect each other. If they
do, then it is a parallelogram. Or, you could find the lengths of all the sides. Let’s do this option.