Q. In the figure alongside, PQRS is a parallelogram. X and Y are any points on QR and RS respectively such that XY||QS. Prove that, Area of triangle PQX = Area of triangle PSY

Soln:

i.                     D PQR = D PSR                                                    i. PR divides ||gm area into equal parts. 

ii.                   X and Y are midpoints (i.e. QX = XR and SY = YR)  ii. XY || QS

iii.                  PX and PY are medians                                            iii. From statement (ii)

iv.                 DPQX + DPXR = DPSY + DPYR                                     iv. From statements (i) and (iii)

v.                   2DPQX = 2DPSY                                                           v. From statements (iii) and (iv)

                      DPQX = DPSY

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