Which of the following is/are not true about the median of a trapezoid?
(a) The median connects the endpoints of the bases of a trapezoid.
(b) The length of the median is half the sum of the lengths of the bases.
(c) The length of the median is half the difference between the lengths of the bases.
(d) The median connects the midpoints of the legs of a trapezoid.

Solution:

A trapezoid is a four-sided closed 2D figure which has an area and its perimeter. Two sides of a trapezoid are parallel to each other and they are termed as the bases of the trapezoid.

A trapezoid is referred to as the quadrilateral with one pair of parallel sides. The parallel sides are known as its bases and the non-parallel sides are known as its legs.

Types of trapezoid:

There are three different types of trapezoid:

1) Scalene trapezoid: When neither the sides nor the angles of the trapezoid are equal, then it is a scalene trapezoid.

2) Right trapezoid:  It is also called the right-angled trapezoid if it has a pair of right angles.

3) Isosceles trapezoid: If the legs or non-parallel sides of the trapezoid are equal in length, then it is called an isosceles trapezoid. The angles of the parallel sides (base) in the isosceles trapezoid are equal to each other.

Properties of the median of the trapezoid:

There are two main properties of the median of a trapezoid. They are:

1) The median connects the midpoints of the legs of a trapezoid.

2) The length of the median is half the sum of the lengths of the bases.

In the figure given below, UT is the median of trapezium PQRS.

Thus, Options (a) and (c) are not true about the median of a trapezoid.

Which of the following is/are not true about the median of a trapezoid?

Summary:

Options (a) and (c) are not true about the median of a trapezoid.