Question

in the diagram of the staircase shown, qt ∥ rs, qt = rs = 9 feet, qr = 3 feet, and m∠qrs = 1
a. which theorem can you use to show that qrst is a parallelogram?
parallelogram opposite angles theorem
opposite sides parallel and congruent theorem
parallelogram opposite angles converse
parallelogram diagonals theorem

Explanation:

To determine the theorem for showing \( QRST \) is a parallelogram, we analyze the given: \( QT \parallel RS \) and \( QT = RS \). The "Opposite Sides Parallel and Congruent Theorem" states that if one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram. Here, \( QT \) and \( RS \) are opposite sides with \( QT \parallel RS \) and \( QT = RS \), so this theorem applies. The other options do not fit: the Opposite Angles Theorem/Corollary relates to angles, and the Diagonals Theorem relates to diagonals, neither of which is the focus here.

Answer:

B. Opposite Sides Parallel and Congruent Theorem