Can rhombus be a trapezoid?

2 Answers
Oct 4, 2017

Rhombus can never be a trapezoid.


Differences between rhombus and trapezoid :
Rhombus : a) opposite sides are parallel. b) all four sides are equal. c) opposite angles are equal. d) special form of rhombus is square where all the four angles are right angles.
Trapezoid : a) only one pair of opposite sides are parallel. b) but the parallel sides are not equal. c) rather all the four sides need not be equal.

Oct 4, 2017

Please see below.


For a trapezoid what one needs is that one pair of opposite sides are parallel - #ul("note only one pair of sides"#. Generally other pair of line are not taken as parallel, however, other pair of sides may or may not be equal and / or parallel.

In a rhombus what we have is that (1) both pairs of opposite sides are parallel and (2) all the sides are equal. Hence, opposite angles too are equal and diagonals bisect each other at right angles.

As a rhombus satisfies the conditions of trapezoid and hence satisfies all properties of trapezoid, we can consider it as a trapezoid too.