Question

Is the short diagonal of a rhombus the same length as the sides of that same rhombus? Or is this not always the case?

Answer 1

NOT ALWAYS

`color(crimson)("Only when one pair of opposite angles equals " pi/3, " shorter diagonal is equal to the side of the rhombus."`

Explanation:

NOT ALWAYS

`color(crimson)("Only when one pair of opposite angles equals " pi/3, " shorter diagonal is equal to the side of the rhombus."`

Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides with all four sides equal.

Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals.

It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure.

From the figure we can see diagonals of a rhombus bisect each other at right right angles. Also diagonals bisect each corner angle.

To find the area of a rhombus, multiply the lengths of the two diagonals and divide by 2 : `(1/2) d_1 * d_2`