http://www.ck12.org Chapter 6. Polygons and Quadrilaterals
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.
RS=
√
(− 5 − 2 )^2 +( 7 − 6 )^2 ST=
√
( 2 − 5 )^2 +( 6 −(− 3 ))^2
=
√
(− 7 )^2 + 12 =
√
(− 3 )^2 + 92
=
√
50 = 5
√
2 =
√
90 = 3
√
10
RV=
√
(− 5 −(− 4 ))^2 +( 7 − 0 )^2 V T=
√
(− 4 − 5 )^2 +( 0 −(− 3 ))^2
=
√
(− 1 )^2 + 72 =
√
(− 9 )^2 + 32
=
√
50 = 5
√
2 =
√
90 = 3
√
10
From this we see that the adjacent sides are congruent. Therefore,RST Vis a kite.
Algebra Review:When asked to “simplify the radical,” pull all square numbers (1, 4, 9, 16, 25, ...) out of the
radical. Above
√
50 =
√
25 ·2. We know√
25 =5, so√
50 =
√
25 · 2 = 5
√
2.
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/52575CK-12 Foundation: Chapter6QuadrilateralClassificationB