Question

all of the following are properties of parallelograms except...
consecutive angles are supplementary
opposite sides are parallel
opposite angles are congruent
diagonals bisect each pair of opposite angles

Explanation:

To determine the incorrect property of a parallelogram, we analyze each option:

1. Consecutive angles are supplementary: In a parallelogram, consecutive angles are supplementary (their sum is \(180^\circ\)) because the opposite sides are parallel, and this follows from the properties of parallel lines cut by a transversal. This is a valid property.
2. Opposite sides are parallel: By definition, a parallelogram is a quadrilateral with both pairs of opposite sides parallel. This is a fundamental property.
3. Opposite angles are congruent: In a parallelogram, opposite angles are equal (congruent). This can be proven using the properties of parallel lines and transversals (alternate interior angles, etc.). This is a valid property.
4. Diagonals bisect each pair of opposite angles: This is not a general property of all parallelograms. This property is specific to rhombuses (a type of parallelogram with all sides equal). In a general parallelogram (like a rectangle or a non - rhombus parallelogram), the diagonals do not bisect the angles. For example, in a rectangle, the diagonals are equal in length but do not bisect the right angles (unless the rectangle is a square, which is a special case of a rhombus).

Answer:

Diagonals bisect each pair of opposite angles