6.4. Quadrilaterals that are Parallelograms http://www.ck12.org
Guided Practice
- What value ofxwould makeABCDa parallelogram?
- Is the quadrilateralRST Ua parallelogram?
- If a quadrilateral has one pair of parallel sides is it a parallelogram?
Answers:
1.AB||DCfrom the markings. Therefore,ABCDwould be a parallelogram ifAB=DCas well.
5 x− 8 = 2 x+ 13
3 x= 21
x= 7In order forABCDto be a parallelogram,xmust equal 7.
- Let’s use the Parallelogram Diagonals Converse to determine ifRST Uis a parallelogram. Find the midpoint of
each diagonal.
Midpoint ofRT=
(− 4 + 3
2 ,
3 − 4
2)
= (− 0. 5 ,− 0. 5 )
Midpoint ofSU=
( 4 − 5
2 ,
5 − 5
2)
= (− 0. 5 , 0 )
Because the midpoint is not the same,RST Uis not a parallelogram.
- Although it has one pair of parallel sides, this quadrilateral is not a parallelogram because its opposite sides are
not necessarily congruent.
Practice
For questions 1-11, determine if the quadrilaterals are parallelograms. If they are, write a reason.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.For questions 12-14, determine the value ofxandythat would make the quadrilateral a parallelogram.
12.
13.
14.For questions 15-17, determine ifABCDis a parallelogram.
15.A( 8 ,− 1 ),B( 6 , 5 ),C(− 7 , 2 ),D(− 5 ,− 4 )