Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
Properties of rhombi often show up in geometric proofs and many other types of problems. All parallelogram properties apply to rhombus properties since a rhombus is a type of parallelogram. In a rhombus, there are (1) two pairs of parallel sides, (2) four sides that are all congruent to each other, (3) diagonals that bisect the angles, and (4) diagonals that are perpendicular bisectors of each other.
It's important to know the properties of a rhombus. Why? Because you're going to use it in proofs, true and false questions, matching, lots of things, especially when you are trying to find missing angles and sides within a rhombus. So let's get started.
The first key thing about a rhombus is that it's a parallelogram. So everything that applies to a parallelogram also applies to a rhombus. So we have two pairs of parallel sides. We also have four sides that are all congruent to each other, not two pairs of congruent sides like a rectangle.
The second key thing is that the diagonals bisect the angles. So if I drew in a diagonal here, it will bisect this angle into two congruent angles and it'll do the same thing to that angle. So these four angles will all be congruent to each other. If I drew in the other diagonal it will bisect that angle and it will bisect this angle as well.
Another key thing is that the diagonals are perpendicular bisectors of each other. So they will always intersect at a 90 degree angle and they're going to bisect each other. So the diagonals of a parallelogram bisect each other but they don't necessarily intersect at a right angle. A rhombus it has to intersect at a 90 degree angle.
So, just to remind you, these two things are not true for rectangles. So for a rectangle the diagonals do not bisect their angles and the diagonals in a rectangle are not perpendicular bisectors of each other.