Question

vera wants to prove that any rectangle is also a parallelogram.

select the appropriate rephrased statement for veras proof.
choose 1 answer:
a in quadrilateral (abcd), if (overline{ab} parallel overline{dc}) and (overline{ad} parallel overline{bc}), then (mangle a = mangle b = mangle c = mangle d = 90^circ).
b in quadrilateral (abcd), if (mangle a = mangle b = mangle c = mangle d = 90^circ), then (overline{ab} parallel overline{dc}) and (overline{ad} parallel overline{bc}).
c in quadrilateral (abcd), if (overline{ab} cong overline{dc}) and (overline{ad} cong overline{bc}), then (mangle a = mangle b = mangle c = mangle d = 90^circ).
d in quadrilateral (abcd), if (mangle a = mangle b = mangle c = mangle d = 90^circ), then (overline{ab} cong overline{dc}) and (overline{ad} cong overline{bc}).

Explanation:

To prove a rectangle is a parallelogram, we need to show that opposite sides are parallel (a key property of parallelograms). A rectangle has all angles equal to \(90^\circ\).

• Option A: Assumes parallel sides to prove right angles, which is the reverse of what we need (we need to prove parallel sides from right angles).
• Option B: States that if all angles are \(90^\circ\) (defining a rectangle), then opposite sides (\(\overline{AB}\) and \(\overline{DC}\), \(\overline{AD}\) and \(\overline{BC}\)) are parallel. This matches the goal of proving a rectangle (all right angles) is a parallelogram (opposite sides parallel).
• Option C: Assumes equal sides to prove right angles, not related to proving parallel sides.
• Option D: Assumes right angles to prove equal sides, not about parallel sides.

Answer:

B. In quadrilateral \(ABCD\), if \(m\angle A = m\angle B = m\angle C = m\angle D = 90^\circ\), then \(\overline{AB} \parallel \overline{DC}\) and \(\overline{AD} \parallel \overline{BC}\).