Question

PQRS is a parallelogram. Q and S are joined to any point M on the diagonal PR of the parallelogram. Prove that area of tringle PQM = area of triangle PSM.

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

construction: draw QX perpendicular on PR and SY perpendicular on PR

Now, in triangle PQX and RSY,

PQ = SR (S)    ( opposite side of parallelogram)

Angle XPQ= Angle YRS   (alternate angles)

angle PXQ = angle RYS   (both 90 degree)

therefore, triangle PQX and RSY are congruent  (by S.A.A rule)

so, QX = SY   equation(i)

we know,

area of triangle = 1/2*base*height

ar of tri PQM = 1/2*PM*QX       equation(ii)

ar of tri PSM = 1/2*PM*SY  (from equation(i))

                     = 1/2*PM*QX       equation(iii)

from eqn(ii) and (iii)

area of tri PQM = area of tri PSM

                                                            PROVED