Question

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

Explanation:

The Diagonals of a Parallelogram Theorem states that the diagonals of a parallelogram bisect each other. In parallelogram \(PQRS\), if the diagonals are \(PR\) and \(QS\) intersecting at \(T\), then \(PT\cong RT\) and \(QT\cong ST\), not \(PT\cong QT\).

Answer:

No, Floyd is not correct. The Diagonals of a Parallelogram Theorem says the diagonals bisect each other so \(PT\) is congruent to the other half of the same - diagonal (\(RT\)), not to \(QT\) which is part of the other diagonal.