Question

question 4 of 10
which of these statements describe properties of parallelograms? check all that apply.

a. opposite sides are congruent.

b. opposite angles are congruent.

c. consecutive angles are supplementary.

d. opposite angles are parallel.

e. diagonals bisect each other.

f. opposite sides are parallel.

Explanation:

• Option A: By the definition and properties of a parallelogram, in a parallelogram, opposite sides are equal (congruent). This is a fundamental property.
• Option B: Opposite angles in a parallelogram are congruent. This can be proven using the properties of parallel lines and transversals (since opposite sides are parallel, alternate - interior angles are equal, leading to opposite angles being congruent).
• Option C: Consecutive angles in a parallelogram are supplementary. Since opposite sides are parallel, consecutive angles are same - side interior angles, and same - side interior angles are supplementary.
• Option D: Angles are not parallel. Parallelism is a property of lines, not angles. So this statement is incorrect.
• Option E: The diagonals of a parallelogram bisect each other. This can be proven using triangle congruence (by showing that the triangles formed by the diagonals are congruent).
• Option F: The definition of a parallelogram is a quadrilateral with two pairs of opposite sides parallel. So this is a defining property.

Answer:

A. Opposite sides are congruent,
B. Opposite angles are congruent,
C. Consecutive angles are supplementary,
E. Diagonals bisect each other,
F. Opposite sides are parallel