Question

select all the correct answers. which statements are always true for a rectangle? the diagonals are congruent. all sides are congruent. the diagonals of a rectangle are perpendicular to each other all angles are congruent the opposite sides are parallel.

Explanation:

• Diagonals are congruent: In a rectangle, using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a\) and \(b\) are the sides of the rectangle and \(c\) is the diagonal), since opposite sides are equal (\(a = a\), \(b = b\)), the diagonals are equal in length (congruent).
• All sides are congruent: In a rectangle, only opposite sides are congruent. A square (a special - case of a rectangle) has all sides congruent, but a general rectangle does not.
• Diagonals are perpendicular: Diagonals are perpendicular in a square (a special rectangle) but not in a general rectangle. The product of the slopes of the diagonals is not \(- 1\) for a non - square rectangle.
• All angles are congruent: All angles in a rectangle are right angles (\(90^{\circ}\)), so they are congruent.
• Opposite sides are parallel: By the definition of a parallelogram (a rectangle is a parallelogram), opposite sides are parallel.

Answer:

• The diagonals are congruent.
• All angles are congruent.
• The opposite sides are parallel.