Question

Quadrilateral QRST has vertices at Q(−1,5), R(2,8), S(4,4), and T(1,1). The measure of Angle Q is 108° and the measure of angle R is 108−2x

Is this a parallelogram?

1-yes

2-no

(1 point)

Answer 1

1 — yes.

Reason: QR slope = (8−5)/(2−(−1)) = 3/3 = 1 and ST slope = (1−4)/(1−4) = −3/−3 = 1, so QR ∥ ST.
RS slope = (4−8)/(4−2) = −4/2 = −2 and QT slope = (1−5)/(1−(−1)) = −4/2 = −2, so RS ∥ QT.
Both pairs of opposite sides are parallel, so QRST is a parallelogram.