Question

in fig.1 ,AM and CN are perpendicular to the diagonal BD of a parallelogram ABCD. prove that AM=CN

Answer 1

in triangle AMB and triangle DNC
AB=DC(opp. sides of parallelogram is equal)
angle AMB =angle DNC (both 90)
angle abm =angle cdb (alternate angles)
so, AMB congurent DBC by(AAS)
AM=CN by(cpct)

Answer 2

AM = CN if AM and CN are perpendicular to the diagonal BD of a parallelogram ABCD

Step-by-step explanation:

AM and CN are perpendicular to the diagonal BD of a parallelogram ABCD

In a Parallelogram ABCD

AB = CD

BC = AD

BD is diagonal

ΔABD & ΔCDB

AB = CD

AD = CB

BD = BD ( common)

ΔABD ≅ ΔCDB

Area of ΔABD = Area of  ΔCDB

AM and CN are perpendicular to the diagonal BD

=> Area of ΔABD = (1/2) BD * AM

   Area of  ΔCDB =  (1/2) BD * CN

(1/2) BD * AM =  (1/2) BD * CN

=> AM = CN

QED

Proved

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