# Parallelogram

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• 10-03-2002
NavyBlue
Parallelogram
Hey, guys, I need a little help with this extra credit problem...

How do you prove the diagonals of a parallelogram are perpendicular to each other, meaning that the diagonals' slopes are negative reciprocal of each other.

And prove the diagonals bisect each other, having the same midpoint?
• 10-03-2002
kermi3
Well...you shouldn't be getting help on a graded assignment to start. But I would look at what happens when you drop an altitude.
• 10-03-2002
NavyBlue
There are 4 coordinates: A = (0,b), B = (-c, 0), C = (a+c,b) D = (a,0)

I tried to find the slopes of diagonal lines AB and BC, but they're not negative reciprocal to each other.
• 10-03-2002
Cshot
That's because AB and BC are not diagonals. AD and BC are. Heheh draw it out man ;)
• 10-03-2002
kermi3
Drop an altitude between the parrallel sides at a 90 degree angle. Do it on your own from there.
• 10-03-2002
NavyBlue
Sorry, guys. I mistyped, not lines AB and BC, but diagonal lines AD and BC. The problem is that I can't really find the slope of BC.

slope of AD = (0 - b) / (a - 0)
= -b/a

slope of BC = (b - 0) / ((a+c) - -c)
= b / a + 2c ?

Aren't the two slopes supposed to be negative recripocal of each others?
• 10-03-2002
kermi3
Look, I'm not going to help you at all anymore....But here's a suggestion...

Do your own work. It's graded, for credit? Don't you think it's cheating to be asking for help?
• 10-03-2002
Fountain
well, it could show initiative
• 10-03-2002
kermi3
You're right it could. However, I think that most teachers would see it as cheating. If it's graded you should do your own work and be proud of it....My opinion...I'm not closing the thread or anything, everyone must make their own choices.
• 10-03-2002
Cshot
If you can prove they are perpendicular, please let me know :D
• 10-03-2002
Cshot
hint hint
• 10-03-2002
kermi3
They aren't parrallel there...he means a parallelogram:
• 10-03-2002
MethodMan
Dont know if this will help but:

From the red lines, if you know they are parallel, then the angles are the same according to the Z pattern.
• 10-03-2002
Cshot
Yes it is. A rectangle is a special kind of parallelogram.
Quote:

Parallelogram

A quadrilateral whose opposite sides are parallel
The opposite sides of a parallelogram are parallel.
A diagonal of a parallelogram divides it into two congruent triangles.
The opposite sides of a parallelogram are congruent.
The opposite angles of a parallelogram are congruent.
The consecutive angels of a parallelogram are supplementary.
The diagonals of a parallelogram bisect each other.
Five ways to prove a quadrilateral is a Parallelogram
1. A quadrilateral is a parallelogram if its opposite sides are parallel.
2. A quadrilateral is a parallelogram if its opposite sides are congruent.
3. A quadrilateral is a parallelogram if two sides are congruent and parallel.
4. A quadrilateral is a parallelogram if its opposite angles are congruent.
5. A quadrilateral is a parallelogram if its diagonals bisect each other.

Rectangle
An equiangular parallelogram
Rhombus
An equilateral parallelogram
Square
An equilateral and equiangular parallelogram
• 10-03-2002
kermi3
Bah you win Cshot. But when proving a therom like this you shouldn't use a "special kind". You should use the most generic you have.
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