Question

Which biconditional statement is valid?

a) A quadrilateral is a square if and only if its diagonals bisect each vertex.
b) Two polygons are congruent if and only if all corresponding parts are congruent.
c) A quadrilateral is a rectangle if and only if its diagonals bisect each other.
d) Nelly

Answer 1

Option (b) 'Two polygons are congruent if and only if all corresponding parts are congruent' is the valid biconditional statement, as it outlines the necessary and sufficient condition for polygon congruence.

Step-by-step explanation:

The correct answer to the question is option (b): Two polygons are congruent if and only if all corresponding parts are congruent. This means that for two polygons to be considered congruent, their corresponding sides must be equal in length, and their corresponding angles must be equal in measure. If any of these conditions do not hold, the polygons are not congruent.

The other options are not correct because the definition of a square does not include the diagonals bisecting each vertex (option a), a quadrilateral can be a rectangle without the diagonals bisecting each other (option c), and option (d) is incomplete and unrelated.