I need to prove a parallelogram is a rhombus using the diagonals, but the diagonals aren't pre drawn on the figure. When I draw the diagonals (and midpoint) do I need a corresponding statement ?

Question

ikram002p · Answer

a parallelogram is a rhombus is wrong sentence
all rhombus r   parallelogram  but not all   parallelogram is a rhombus

ikram002p · Answer

ao to prove it in general is impossiple but if u have a qs just type it

anonymous · Answer

@ikram002p
Yeah, not all parallelograms are rhombus..

phi · Answer

Do they give you any info about the diagonals ?

phi · Answer

you can  say "draw the diagonals" for the corresponding statement.

But you need some more info about the diagonals. i.e. they tell you the diagonals are perpendicular to each other.

anonymous · Answer

Here is the given info: The coordinates of the vertices of parallelogram ABCD are A(-4,5), B(1,4), C(2,-1), and D(-3,0). Using the diagonals, prove that ABCD is a rhombus.
The figure does not have pre drawn diagonals so I have to draw them, my question is do I need a theorem or postulate to add the diagonals to the figure?

phi · Answer

you should just note that you added the diagonals.  Reason:  you can draw a line between any 2 points.

I am thinking that you want to show that the diagonals are perpendicular to each other. (that means you have a rhombus)

to show the diagonals are perpendicular, find the line through the 2 pts that define the diagonal.  Do that for the other diagonal.  show that the slopes are negative reciprocals.

Or you could use the distance formula and show all 4 sides have the same length (then no need for the diagonals)