Question

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

Explanation:

• Diagonals congruent: By the property of rectangles, the diagonals are of equal length (\(AC = BD\) in rectangle \(ABCD\)).
• Opposite sides parallel: A rectangle is a parallelogram, and in a parallelogram (including rectangles), opposite sides are parallel (\(AB\parallel CD\) and \(AD\parallel BC\)).
• All angles congruent: In a rectangle, each angle is \(90^{\circ}\), so \(\angle A=\angle B=\angle C=\angle D = 90^{\circ}\).

• Diagonals perpendicular: This is a property of a rhombus (and square, which is a special case of rhombus). In a general rectangle, the diagonals are not perpendicular. For example, in a non - square rectangle with length \(l

eq\) width \(w\), using the slope formula or vector dot - product (if we consider coordinate geometry), we can show the diagonals are not perpendicular.

• All sides congruent: This is a property of a square. In a general rectangle, length \(l\) and width \(w\) are not equal (\(l

eq w\) in a non - square rectangle).

Answer:

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