Question

The Diagonals of a parallelogram are 2.3cm and 3.2cm long. Can you tell if the parallelogram is a rhombus? Explain.

Answer 1

in order to be a rhombus, all sides must have equal length. are the lengths of the two sides 2.3 and 3.2 equal length?

http://www.mathsisfun.com/geometry/rhombus.html

Answer 2

Please see the attached diagram.

A rhombus has four equal sides. The circle has a diameter of 3.2 cm and represents the locus of points that might be occupied by the ends of the longer diagonal given. So CG is half 3.2 cm. The triangle above the number line represents just half of the parallelogram that can be drawn with the parallel lines given by (0,0) to G and the line that you must imagine and the parallel line given by GB and the other line that you must imagine.

Notice that as G moves along the circle it's always possible to imagine the parallel lines and the diagonals of the parallelogram maintain their constant lengths. However, the four sides of the parallelogram are usual non-equal.

You might be interested in knowing that I used Geogebra to construct this diagram. It's free on the web.