1. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that: (i) SR || AC and SR = 1/2 AC (ii) PQ = SR (iii) PQRS is a parallelogram.
Solution: (i) In ΔDAC, R is the mid point of DC and S is the mid point of DA. Thus by mid point theorem, SR || AC and SR = ½ AC (ii) In ΔBAC, P is the mid point of AB and Q is the mid point of BC. Thus by mid point theorem, PQ || AC and PQ = ½ AC also, SR = ½ AC , PQ = SR (iii) SR || AC ———————- from question (i) and, PQ || AC ———————- from question (ii) ⇒ SR || PQ – from (i) and (ii) also, PQ = SR , PQRS is a parallelogram.
ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagona
