CK-12 Geometry-Concepts

6.8. Quadrilateral Classification http://www.ck12.org

All four sides are equal. That means, this quadrilateral is either a rhombus or a square. The difference between the
two is that a square has four 90◦angles and congruent diagonals. Let’s find the length of the diagonals.

EG=

√

( 5 − 5 )^2 +(− 1 −(− 5 ))^2 F H=

√

( 11 −(− 1 ))^2 +(− 3 −(− 3 ))^2

=

√

02 + 42 =

√

122 + 02

=

√

16 = 4 =

√

144 = 12

The diagonals are not congruent, soEF GHis a rhombus.

Interactive Practice

MEDIA

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URL: http://www.ck12.org/flx/render/embeddedobject/113034

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1. If a quadrilateral has exactly one pair of parallel sides, what type of quadrilateral is it?


2. If a quadrilateral has two pairs of parallel sides and one right angle, what type of quadrilateral is it?


3. If a quadrilateral has perpendicular diagonals, what type of quadrilateral is it?


4. If a quadrilateral has diagonals that are perpendicular and congruent, what type of quadrilateral is it?


5. If a quadrilateral has four congruent sides and one right angle, what type of quadrilateral is it?

Determine what type of quadrilateralABCDis.

6.A(− 2 , 4 ),B(− 1 , 2 ),C(− 3 , 1 ),D(− 4 , 3 )

7.A(− 2 , 3 ),B( 3 , 4 ),C( 2 ,− 1 ),D(− 3 ,− 2 )

8.A( 1 ,− 1 ),B( 7 , 1 ),C( 8 ,− 2 ),D( 2 ,− 4 )

9.A( 10 , 4 ),B( 8 ,− 2 ),C( 2 , 2 ),D( 4 , 8 )

10.A( 0 , 0 ),B( 5 , 0 ),C( 0 , 4 ),D( 5 , 4 )

11.A(− 1 , 0 ),B( 0 , 1 ),C( 1 , 0 ),D( 0 ,− 1 )

12.A( 2 , 0 ),B( 3 , 5 ),C( 5 , 0 ),D( 6 , 5 )

SRU Eis a rectangle andPRUCis a square.

13. What type of quadrilateral isSPCE?


14. IfSR=20 andRU=12, findCE.


15. FindSCandRCbased on the information from part b. Round your answers to the nearest hundredth.