Rhombus — Geometry, what it means and where it is taught
A parallelogram with four congruent sides.
Taught in Geometry.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Parallelogram — A quadrilateral with both pairs of opposite sides parallel.
- Congruent — Same size and same shape. Written △ ABC ≅ △ DEF.
Practise this idea
5 questions in the course bank use Rhombus, in How to Write a Proof, Quadrilaterals & Polygon Properties.
Problem 1
Give a counterexample to "all quadrilaterals with four equal sides are squares".
Worked answer
a rhombus
A rhombus has four equal sides.
Its angles need not be right angles.
Problem 2
Is every square a rectangle?
- Yes
- No
- Only if it is also a rhombus
- Only in coordinate geometry
Worked answer
Yes
A square is a parallelogram with four right angles.
That is exactly a rectangle, plus equal sides.
Problem 3
Congruent diagonals that bisect each other mean the shape is a
- rectangle
- rhombus
- trapezoid
- kite
Worked answer
rectangle
Bisecting diagonals make it a parallelogram.
Congruent diagonals upgrade it to a rectangle.
Problem 4
Perpendicular diagonals that bisect each other mean the shape is a
- rhombus
- rectangle
- trapezoid
- square
Worked answer
rhombus
Bisecting makes it a parallelogram.
Perpendicular makes it a rhombus.
Problem 5
A quadrilateral has diagonals that bisect each other, are congruent, and are perpendicular. Name it.
Worked answer
square
Bisecting: parallelogram.
Congruent: rectangle. Perpendicular: rhombus.
Both together: a square.