Question

1. critique reasoning pqrs is a parallelogram. floyd states that he knows that pt≅qt by the diagonals of a parallelogram theorem. is floyd correct? explain your reasoning.

Explanation:

Step1: Recall diagonals of parallelogram property

The diagonals of a parallelogram bisect each other. That is, if \(PQRS\) is a parallelogram with diagonals \(PR\) and \(QS\) intersecting at \(T\), then \(PT = TR\) and \(QT=TS\).

Step2: Analyze Floyd's statement

Floyd says \(\overline{PT}\cong\overline{QT}\) by the Diagonals of a Parallelogram Theorem. But the Diagonals of a Parallelogram Theorem only guarantees that the diagonals bisect each other (i.e., \(PT = TR\) and \(QT = TS\)), not that \(PT=QT\). So Floyd is incorrect.

Answer:

No, Floyd is not correct. The Diagonals of a Parallelogram Theorem states that the diagonals of a parallelogram bisect each other, not that one - half of one diagonal is congruent to one - half of the other diagonal.