If two parallel lines are intersected by a transversal, then the bisectors of the two interior angles on the same side of the transversal are drawn. The figure enclosed by these four bisectors is a:

Introduction / Context:Two parallel lines cut by a transversal form two interior (co-interior) angles that are supplementary (sum to 180°). If we construct the angle bisectors for each pair of interior angles on both parallel lines, we examine the shape enclosed by these four bisectors.

Given Data / Assumptions:

• Lines l₁ ∥ l₂ and a transversal t.
• Interior angles on the same side of t are supplementary.
• For each pair, we draw their internal bisectors.

Concept / Approach:

• If two angles are supplementary (α and 180°−α), their bisectors are perpendicular because they are at α/2 and 90°−α/2 apart ⇒ total separation 90°.
• On each parallel line, the two bisectors formed with the transversal are perpendicular lines.
• Because corresponding interior angles on parallel lines are equal, the bisector lines on l₁ are parallel to their counterparts on l₂.

Step-by-Step Reasoning:

Verification / Alternative check:Choose α = 60° for concreteness. Bisectors at 30° and 60° from the transversal’s complement produce a rectangle in any coordinate construction consistent with l₁ ∥ l₂.

Why Other Options Are Wrong:

• Trapezium: has only one pair of parallel sides.
• Square: would additionally require equal adjacent side lengths; not guaranteed.
• Circle: not a polygonal enclosure by straight bisectors.
• None of these: Not applicable; rectangle is correct.

Common Pitfalls:

• Thinking the bisectors themselves must be at 45°; they depend on α but remain mutually perpendicular for supplementary pairs.

Final Answer:Rectangle