ABCD is a trapezium and P, Q are the mid-points of the diagonals AC and BD. Then PQ is equal to

In a trapezium, the line segment connecting the midpoints of the diagonals is equal to half the sum of the lengths of the bases.

Here's the step-by-step solution:

Step 1: Let's denote the lengths of the bases (the parallel sides) of the trapezium ABCD as a and b (AD = a, BC = b), and the lengths of the diagonals as d1 and d2 (AC = d1, BD = d2).

Step 2: The midpoints of the diagonals divide each diagonal into two segments of equal length. Therefore, AP = PC = d1/2 and BQ = QD = d2/2.

Step 3: Since P and Q are the midpoints of the diagonals, the line segment PQ is parallel to both bases of the trapezium.

Step 4: In a trapezium, the line segment connecting the midpoints of the diagonals is equal to half the sum of the lengths of the bases. Therefore, PQ = 1/2 * (a + b).

So, without knowing the specific lengths of the sides of the trapezium, we can say that the length of line segment PQ is half the sum of the lengths of the bases.