Question

19 for a rectangle, which of the following are true? (select all that apply) a all sides are congruent b all angles are right angles c opposites sides are congruent d diagonals are congruent e opposite sides are parallel f consecutive sides are congruent

Explanation:

• Option A: In a rectangle, only opposite sides are congruent, not all sides. A square (a special rectangle) has all sides congruent, but a general rectangle does not. So, this option is false.
• Option B: By the definition of a rectangle, all four angles are right angles (\(90^{\circ}\)). So, this option is true.
• Option C: One of the properties of a rectangle is that opposite sides are congruent. So, this option is true.
• Option D: The diagonals of a rectangle are congruent. Using the Pythagorean theorem \(d_1=\sqrt{l^{2}+w^{2}}\) and \(d_2=\sqrt{l^{2}+w^{2}}\) (where \(l\) is the length and \(w\) is the width of the rectangle), we can show that the two diagonals are equal in length. So, this option is true.
• Option E: A rectangle is a parallelogram, and in a parallelogram (and thus in a rectangle), opposite sides are parallel. So, this option is true.
• Option F: Consecutive sides (adjacent sides) of a rectangle are not congruent in a general rectangle (only in a square, which is a special case). So, this option is false.

Answer:

B. All angles are right angles, C. Opposites sides are congruent, D. Diagonals are congruent, E. Opposite sides are parallel