Use the diagonals to determine whether a parallelogram with vertices P(2,4), E(4,8), S(12,4), and T(10,0) is a rectangle, rhombus, or square. Give all the names that apply. PS = ET, so PEST is a rectangle. The slope of PS = 0 and the slope of ET = −4/3, so the diagonals are not perpendicular. Therefore, PEST is not a rhombus, nor a square.

PS ≠ ET, so PEST is neither a rectangle nor a square. The slope of PS = 0 and the slope of ET = −4/3, so PEST is a rhombus.

PS = ET, so PEST is a rectangle or a square. The slope of PS = 3/4 and the slope of ET = −4/3, so PS ⊥ ET. PEST is a square.

PS = ET, so PEST is a rectangle or a square. The slope of PS = 0 and the slope of ET = −4/3, so the diagonals are not perpendicular. PEST is a square.