SOLUTION: Given a parallelogram MNOP in which PN= 32 cm and OM = 24 cm.State the length PS and OS. (The middle letter of the parallelogram is S)

Algebra ->  Parallelograms -> SOLUTION: Given a parallelogram MNOP in which PN= 32 cm and OM = 24 cm.State the length PS and OS. (The middle letter of the parallelogram is S)      Log On


   

Question 979444: Given a parallelogram MNOP in which PN= 32 cm and OM = 24 cm.State the length PS and OS.
(The middle letter of the parallelogram is S)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The two diagonals intersect at point S.
(That must be what you meant when you wrote that the "middle letter of the parallelogram is S").

A property of parallelograms is that
"diagonals bisect each other",
meaning that they intersect at their midpoint.
So, S is the midpoint of diagonal PN, and the midpoint of diagonal OM .
Since S is the midpoint of PN , PN=PS%2BSN , and PS=SN ,
Then system%28PN=PS%2BSN%2CPS=SN%29--->PN=PS%2BPS=2PS , and also, since PN=32cm , system%28PN=2PS%2CPN=32cm%29--->2PS=32cm--->PS=32cm%2F2--->highlight%28PS=16cm%29 .
Since S is the midpoint of OM , OM=OS%2BSM , and OS=SM
Then system%28OM=OS%2BSM%2COS=SM%29--->OM=OS%2BOS=2OS , and also, since OM=24cm , system%28OM=2OS%2COM=24cm%29--->2OS=24cm--->OS=24cm%2F2--->highlight%28OS=12cm%29 .