Question

If two parallel lines are intersected by a transversal, bisectors of its interior angles will form

• A. Square
• B. Rhombus
• C. Rectangle
• D. None of these

Hint:

If two parallel lines are intersected by a transversal, bisectors of its interior angles will form

Answer 1

The Correct Option is C

Let the parallel lines be L1 and L2, intersected by transversal T. Consider two con secutive interior angles (e.g., on the same side of T between L1 and L2). Their sum is 180°. Let the angles be and . Their bisectors will meet at an angle calculated as follows: In the triangle formed by the bisectors and the transversal segment between L1 and L2, the angles are 2, 2, and the angle between bisectors (say ). So, 2 + 2 + = 180. Since + = 180, wehave 2 + 2 + = 180, which means 180/2 + = 180,so90 + = 180,and = 90. The quadrilateral formed by the four bisectors of the interior angles has all its angles equal to 90° (by applying this logic to all pairs of consecutive interior angles). A quadrilateral with four right angles is a Rectangle (3). It becomes a square only if the transversal is perpendicular to the parallel lines.