Which of the following statements are true for rectangles?
A. All interior angles are right angles.
B. Diagonals are perpendicular to each other.
C. Diagonals are equal.
D. Opposite angles are supplementary.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A, C and D only
A rectangle is a parallelogram with all four angles right angles; its other properties follow from this.
A. All interior angles are right angles. Correct. This is the defining property of a rectangle: each angle is 90°.
B. Diagonals are perpendicular to each other. Incorrect. The diagonals of a rectangle bisect each other, but they cross at right angles only when the rectangle is a square; this is a property of a rhombus.
C. Diagonals are equal. Correct. Each diagonal is the hypotenuse of a right triangle with the length and breadth as its sides, so both equal \(\sqrt{l^2+b^2}\).
D. Opposite angles are supplementary. Correct. Opposite angles are both 90°, and \(90^\circ+90^\circ=180^\circ\), so they add up to 180°.