Question

prove that two opposite vertices of a parallelogram are equal distance from the diagonal not contain in these vertices​

Answer 1

distance of opposite vertices from the diagonal  not containing these vertices​are equal

Step-by-step explanation:

Let say A & C are oppoiste vertices  & BD is diagonal

Now Δ ABD & Δ CDB

AB = CD   ( opposite sides of parallelogram are equal)

AD = CD  ( opposite sides of parallelogram are equal)

BD = BD   ( common)

=> Δ ABD ≅ Δ CDB

=> Area of Δ ABD = Area of  Δ CDB

Now lets Draw AM ⊥ BD    &   CN ⊥ BD

AM & CN are  distance of vertices from the diagonal

Now area of Δ ABD  = (1/2) BD * AM

Now area of Δ CDB  = (1/2) BD * CN

Area of Δ ABD = Area of  Δ CDB

=>  (1/2) BD * AM = (1/2) BD * CN

=> AM = CN

distance of opposite vertices from the diagonal  not containing these vertices​are equal

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