Question

question 16 of 27
which of the following is a characteristic of all parallelograms?

a. both pairs of opposite sides are congruent.

b. there are 4 right angles.

c. the diagonals are perpendicular.

d. consecutive angles are congruent.

Explanation:

To determine the characteristic of all parallelograms, we analyze each option:

• Option A: By the definition and properties of a parallelogram, one of the fundamental properties is that both pairs of opposite sides are congruent. This holds true for all parallelograms (e.g., rhombus, rectangle, square, and general parallelograms).
• Option B: Having 4 right angles is a property of rectangles (and squares, which are special rectangles), but not all parallelograms. For example, a rhombus that is not a square does not have right angles.
• Option C: Diagonals being perpendicular is a property of rhombuses (and squares), but not all parallelograms. For example, a rectangle that is not a square has diagonals that are congruent but not perpendicular.
• Option D: In a parallelogram, consecutive angles are supplementary (their sum is \(180^\circ\)), not necessarily congruent. Congruent consecutive angles would imply each is \(90^\circ\), which is only true for rectangles, not all parallelograms.

Answer:

A. Both pairs of opposite sides are congruent.