Question

h) B In the given trapezium PQRS, A and B are the mid-points of the diagonals QS and PR respectively. Prove that (ii) AB ( 2 (Hint: Join Q and B and produce QB to meet SR at C) (i) AB // SR and 1/2 (SR-PQ) ​

Answer 1

See the diagram.

PQ is parallel to RS in the trapezium. Given that A is mid point of PR and B is midpoint of QS. Let C be midpoint of PS and D be the midpoint of QR.

CB is line joining midpoints of two sides of the triangle PQS. Hence, CB is parallel to PQ and also PQ = 2 * CB.

Similarly, in triangle PRS, CA is parallel to RS, and RS = 2 * CA Rs = 2 (CB + BA) = PQ + 2 BA

AB = 1/2* (RS - PQ), we assumed that RS is bigger than PQ.

If PQ is longer then RS, then it will be AB = 1/2 (PQ - RS)

For the question 2: We don't know about the locations points L, M, P and Q, You need to enclose a diagram.