Use the diagonals to determine whether a parallelogram with vertices B(2,−2), E(6,−4), S(8,−8), and T(4,−6) is a rectangle, rhombus, or square. Give all the names that apply. BS = TE, so BEST is a rectangle or a square. The slope of BS = −1 and the slope of TE = 1, so BS ⊥ TE. BEST is a rhombus. Since BEST is a rectangle and a rhombus, it is also a square.

BS ≠ TE, so BEST is neither a rectangle nor a square. The slope of BS = 1 and the slope of TE = 1, so the diagonals are not perpendicular. BEST is not a rhombus.

BS ≠ TE, so BEST is neither a rectangle nor a square. The slope of BS = −1 and the slope of TE = 1, so BS ⊥ TE. Therefore, BEST is a rhombus.

BS = TE, so BEST is a rectangle or a square. The slope of BS = −1 and the slope of TE = −1, so the diagonals are not perpendicular. Therefore, BEST is a rectangle.