Question

Which biconditional statement is true?

A shape is a rectangle if and only if the shape has exactly four sides and four right angles.
A shape is a trapezoid if and only if the shape has a pair of parallel sides.
A shape is a triangle if and only if the shape has three sides and three acute angles.
A shape is a square if and only if the shape has exactly four congruent sides.

Answer 1

The first statement is true.

- Rectangle iff it has exactly four sides and four right angles — correct: a rectangle is a quadrilateral with four right angles, and any quadrilateral with four right angles is a rectangle.

The others are false:

- Trapezoid iff it has a pair of parallel sides — ambiguous: some definitions require exactly one pair (which would make the biconditional false because parallelograms have two), others use “at least one pair” (then it would be true). Without a specified convention this is not reliably true.
- Triangle iff it has three sides and three acute angles — false: triangles can be right or obtuse.
- Square iff it has exactly four congruent sides — false: four congruent sides define a rhombus; a square also requires four right angles.