6.2. Properties of Parallelograms http://www.ck12.org
14.m^6 AW E
15.m^6 ESV
16.m^6 W EA
17.m^6 AV WIn the parallelogramSNOW,ST= 6 ,NW= 4 ,m^6 OSW= 36 ◦,m^6 SNW= 58 ◦andm^6 NT S= 80 ◦. (diagram is not
drawn to scale)
18.SO
19.NT
20.m^6 NW S
21.m^6 SOWPlot the pointsE(− 1 , 3 ),F( 3 , 4 ),G( 5 ,− 1 ),H( 1 ,− 2 )and use parallelogramEF GHfor problems 22-25.
- Find the coordinates of the point at which the diagonals intersect. How did you do this?
- Find the slopes of all four sides. What do you notice?
- Use the distance formula to find the lengths of all four sides. What do you notice?
- Make a conjecture about how you might determine whether a quadrilateral in the coordinate is a parallelogram.
Write a two-column proof.
26.Opposite Angles TheoremGiven:ABCDis a parallelogram with diagonalBDProve:^6 A∼=^6 C
27.Parallelogram Diagonals TheoremGiven:ABCDis a parallelogram with diagonalsBDandACProve:AE∼=EC,DE∼=EB