Question

In the trapezium ABCD, P and Q are the mid-points of non-parallel sides AD and BC, respectively. Then PQ is equal to ______.

Options

• `1/2 (AB - CD)`

• `1/2 (AB + CD)`

• `1/3 (AB - CD)`

• `1/3 (AB + CD)`

Answer 1

In the trapezium ABCD, P and Q are the mid-points of non-parallel sides AD and BC, respectively. Then PQ is equal to `underlinebb(1/2 (AB + CD))`.

Explanation:

In trapezium ABCD with AB || CD, the segment joining the midpoints P of AD and Q of BC is parallel to the bases and its length equals half the sum of the bases.

For example, with A(x₁, y₁), B(x₂, y₁), D(x₄, y₂), C(x₃, y₂), we get 

`P = ((x_1 + x_4)/2, (y_1 + y_2)/2)` 

And `Q = ((x_2 + x_3)/2, (y_1 + y_2)/2)` 

So, `PQ = ((x_2 + x_3) - (x_1 + x_4))/2` 

= `(AB + CD)/2`