CK-12 Geometry Concepts

http://www.ck12.org Chapter 6. Polygons and Quadrilaterals

Example B

Is quadrilateralEF GHa parallelogram? How do you know?

For part a, the opposite angles are equal, so by the Opposite Angles Theorem Converse,EF GHis a parallelogram.
In part b, the diagonals do not bisect each other, soEF GHis not a parallelogram.

Example C

Is the quadrilateralABCDa parallelogram?

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

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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.

Vocabulary

Aparallelogramis a quadrilateral with two pairs of parallel sides.