http://www.ck12.org Chapter 6. Polygons and Quadrilaterals
16.A(− 5 , 8 ),B(− 2 , 9 ),C( 3 , 4 ),D( 0 , 3 )
17.A(− 2 , 6 ),B( 4 ,− 4 ),C( 13 ,− 7 ),D( 4 ,− 10 )
Write a two-column proof.
18.Parallelogram Diagonals Theorem ConverseGiven:AE∼=EC,DE∼=EBProve:ABCDis a parallelogram- Given:^6 ADB∼=CBD,AD∼=BCProve:ABCDis a parallelogram
Suppose thatA(− 2 , 3 ),B( 3 , 3 )andC( 1 ,− 3 )are three of four vertices of a parallelogram.
- Depending on where you choose to put pointD, the name of the parallelogram you draw will change. Sketch
a picture to show all possible parallelograms. How many can you draw? - If you know the parallelogram is namedABDC, what is the slope of side parallel toAC?
- Again, assuming the parallelogram is namedABDC, what is the length ofBD?
The pointsQ(− 1 , 1 ),U( 7 , 1 ),A( 1 , 7 )andD(− 1 , 5 )are the vertices of quadrilateralQUAD. Plot the points on graph
paper to complete problems 23-26.
- Find the midpoints of sidesQU,UA,ADandDQ. Label themW,X,YandZrespectively.
- Connect the midpoints to form quadrilateralW XY Z. What does this quadrilateral appear to be?
- Use slopes to verify your answer to problem 24.
- Use midpoints to verify your answer to problem 24.