CK-12 Geometry-Concepts

6.4. Quadrilaterals that are Parallelograms http://www.ck12.org

First, find the length ofABandCD.

AB=

√

(− 1 − 3 )^2 +( 5 − 3 )^2 CD=

√

( 2 − 6 )^2 +(− 2 + 4 )^2

=

√

(− 4 )^2 + 22 =

√

(− 4 )^2 + 22

=

√

16 + 4 =

√

16 + 4

=

√

20 =

√

20

AB=CD, so if the two lines have the same slope,ABCDis a parallelogram.

SlopeAB=−^51 −−^33 =−^24 =−^12 SlopeCD=− 22 −+ 64 =−^24 =−^12

Therefore,ABCDis a parallelogram.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52571

CK-12 Foundation: Chapter6QuadrilateralsthatareParallelogramsB

Concept Problem Revisited

First, we can use the Pythagorean Theorem to find the length of the second diagonal.

902 + 902 =d^2

8100 + 8100 =d^2

16200 =d^2

d= 127. 3

This means that the diagonals are equal. If the diagonals are equal, the other two sides of the diamond are also 90
feet. Therefore, the baseball diamond is a parallelogram.