Question

Identify whether each statement is always, sometimes, or never true.

A parallelogram has four congruent sides.

A square has four right angles.


A trapezoid has one pair of parallel sides.


The diagonals of a rhombus are congruent.

Answer 1

A parallelogram has four congruent sides.
- Sometimes. A parallelogram need not have all sides equal (e.g. a non-square rectangle). It does if it is a rhombus (or square).

A square has four right angles.
- Always. By definition a square is a quadrilateral with four equal sides and four right angles.

A trapezoid has one pair of parallel sides.
- Sometimes. This depends on the definition: if “trapezoid” means “exactly one pair of parallel sides” then it’s always true; if it means “at least one pair of parallel sides” (the inclusive definition), then parallelograms have two pairs and so the statement is not always true.

The diagonals of a rhombus are congruent.
- Sometimes. In a general rhombus the diagonals are perpendicular bisectors but not equal; they are congruent only in the special case that the rhombus is a square.