Register to reply

Prove rhombus

by powp
Tags: prove, rhombus
Share this thread:
Apr2-05, 06:19 AM
P: 93

How do you prove that the diagonals od a rhombus bisect each other??

Phys.Org News Partner Mathematics news on
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
Apr2-05, 07:21 AM
P: 137
when u prove that they make right angles between them.
then, you will get the answer.
180/2 = 90!
Apr2-05, 07:50 AM
P: 93
What I can figure out is that all sides are equal and the oposite corners angles = each other. Not sure what to do

Apr2-05, 08:02 AM
P: 137
Prove rhombus

it is the theory which tells you that in a rombus the diagonals are perpendicular
so far they bisect each other
is it clear?
Apr2-05, 08:49 AM
HW Helper
Curious3141's Avatar
P: 2,943
You can actually prove a stronger result easily using vectors. The diagonals of a parallelogram bisect one another. The rhombus is just a special case of a parallelogram with all sides being equal.

Let the parallelogram be drawn on a Cartesian plane as shown in the diagram, and the sides labelled as vectors as shown. You can see that one diagonal is [tex]\vec a + \vec b[/tex] and the other is [tex]\vec b - \vec a[/tex]

Let [tex]\vec{WO}[/tex] be [tex]k_1(\vec a + \vec b)[/tex]


[tex]\vec{OZ}[/tex] be [tex]k_2(\vec b - \vec a)[/tex]

where [tex]k_1, k_2[/tex] are some scalars (which we are to determine).

In triangle WOZ, you can further see that

[tex]\vec{WZ} = \vec{WO} + \vec{OZ}[/tex]


[tex]\vec b = k_1(\vec a + \vec b) + k_2(\vec b - \vec a)[/tex]

[tex]\vec b = (k_1 - k_2)\vec a + (k_1 + k_2)\vec b[/tex]

giving [tex]k_1 - k_2 = 0[/tex] ---eqn (1)

and [tex]k_1 + k_2 = 1[/tex] ---eqn(2)

Solving those simple simultaneous equations yields [tex]k_1 = k_2 = \frac{1}{2}[/tex]

so you know that the diagonals bisect each other. (QED)
Attached Thumbnails

Register to reply

Related Discussions
Prove that General Math 1
Please prove this Differential Geometry 6
Need help proving an expression of roots of sums including roots General Math 16
Vector Rhombus Proof Calculus & Beyond Homework 2
Prove the following: Introductory Physics Homework 3