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:

Step1: Analyze properties of a rectangle

A rectangle has four right angles (so all angles are congruent as each is \(90^{\circ}\)), opposite sides are parallel (by definition of a parallelogram, and a rectangle is a parallelogram), and the diagonals of a rectangle are congruent (can be proved using triangle congruence, e.g., in rectangle \(ABCD\) with diagonals \(AC\) and \(BD\), \(\triangle ABC\cong\triangle BAD\) by \(SAS\) ( \(AB = BA\), \(\angle ABC=\angle BAD = 90^{\circ}\), \(BC = AD\) ) so \(AC = BD\)).

Step2: Check incorrect statements

• All sides are congruent is false. In a rectangle, only opposite sides are congruent.
• The diagonals of a rectangle are perpendicular to each other is false. This is a property of a rhombus (and a square which is a special case of both a rhombus and a rectangle).

Answer:

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