Question

Complete the following statement with the word always, sometimes, or never.

The diagonals of a trapezoid ___ bisect each other.

Short answer

The diagonals of a trapezoid never bisect each other.

Step-by-step solution

Step 1. Apply the concept of a trapezoid.

A trapezoid is a flat closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and their non-parallel sides are called legs.

Step 2. Step description.

Since a trapezoid is a quadrilateral with only one pair of parallel sides. The parallel sides are called bases and the other sides are legs.

Also, the diagonals of a trapezoid are line segments joining opposite vertices of a trapezoid and if a trapezoid has congruent legs then it is named an isosceles trapezoid.

Diagonals of an isosceles trapezoid are equal in length.

Step 3. Step description.

Since diagonals of an isosceles trapezoid are equal in length thus the diagonals of a trapezoid never bisect each other.

Therefore, the diagonals of a trapezoid never bisect each other.