We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

Given that the diagonals of a rhombus are always perpendicular bisectors of each other, what is the area of a rhombus with side length sqrt89 units and diagonals that differ by 6 units?

Thanks so much!

AnonymousConfusedGuy Mar 22, 2018

#2**+1 **

A quadrilateral is a rhombus if and only if the diagonals are perpendicular bisectors of each other.

This is an "if and only if" proof, so there are two things we have to prove:

One way to prove this is to use congruent triangles.

However, note that this essentially runs through the proof of one of the isosceles triangle theorems which we have already proved. Note the SSS reason after we established the reflexive side. We do not have to do it again. We can simply refer to it.

For the converse,

there is the congruent tirangle proof.

But, again we are running through a proof of one of the isosceles triangle theorems. We could simply refer to it instead of proving it again.

One could also use the fact that a point is equidistant from two given points if and only if it is on the perpendicular bisector of the line segment between them.

Lightning Mar 22, 2018