ABCD Is A Parallelogram. Show That 2DC - DB = AC

Let

AB = a = DC

BC = b = AD

AC and DB be the diagonals {a,b are vectors}

AC + DB

(AB + BC)+ (DA + DC)

(a + b) + (-b + a) {-b as the direction is negative}

= 2a

= 2DC

Therefore,

2DC = AC + DB

2DC – DB = AC

Hence, proved

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