http://www.ck12.org Chapter 6. Polygons and Quadrilaterals
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 more content.CK-12 Foundation: Chapter6QuadrilateralClassificationB
Example D
Is the quadrilateralABCDa parallelogram?
We have determined there are four different ways to show a quadrilateral is a parallelogram in thex−yplane. Let’s
check if a pair of opposite sides are congruent and parallel. 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.
Vocabulary
Aparallelogramis a quadrilateral with two pairs of parallel sides. A quadrilateral is arectangleif and only if it has
four right (congruent) angles. A quadrilateral is arhombusif and only if it has four congruent sides. A quadrilateral
is asquareif and only if it has four right angles and four congruent sides. Atrapezoidis a quadrilateral with exactly
one pair of parallel sides. Anisosceles trapezoidis a trapezoid where the non-parallel sides are congruent. Akite
is a quadrilateral with two distinct sets of adjacent congruent sides. If a kite is concave, it is called adart.
Guided Practice
- A quadrilateral is defined by the four linesy= 2 x+1,y=− 2 x+5,y= 2 x−4, andy=− 2 x−5. Is this
quadrilateral a rectangle? - Determine what type of quadrilateralABCDis.A(− 3 , 3 ),B( 1 , 5 ),C( 4 ,− 1 ),D( 1 ,− 5 ). Simplify all radicals.
- Determine what type of quadrilateralEF GHis.E( 5 ,− 1 ),F( 11 ,− 3 ),G( 5 ,− 5 ),H(− 1 ,− 3 )
Answers: