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 neverbisect 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 as 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.