Can you recreate squares and rhombuses if you are only given a side
or a diagonal?
Take any rectangle ABCD such that AB > BC. The point P is on AB
and Q is on CD. Show that there is exactly one position of P and Q
such that APCQ is a rhombus.
Four rods of equal length are hinged at their endpoints to form a
rhombus. The diagonals meet at X. One edge is fixed, the opposite
edge is allowed to move in the plane. Describe the locus of. . . .
We have four rods of equal lengths hinged at their endpoints to
form a rhombus ABCD. Keeping AB fixed we allow CD to take all
possible positions in the plane. What is the locus (or path) of the
point. . . .
The challenge is to produce elegant solutions. Elegance here
implies simplicity. The focus is on rhombi, in particular those
formed by jointing two equilateral triangles along an edge.
The diagram shows a regular pentagon with sides of unit length.
Find all the angles in the diagram. Prove that the quadrilateral
shown in red is a rhombus.
A rhombus PQRS has an angle of 72 degrees. OQ = OR = OS = 1 unit. Find all the angles, show that POR is a straight line and that the side of the rhombus is equal to the Golden Ratio.
Explore patterns based on a rhombus. How can you enlarge the
pattern - or explode it?