Q. 115.0( 2 Votes )

# Prove that the po

Answer :

**Given:** Points are A(1, 3, 0), B(-5, 5, 2), C(-9, -1, 2) and D(-3, -3, 0)

**To prove:** the quadrilateral formed by these 4 points is a parallelogram but not a rectangle

Opposite sides of both parallelogram and rectangle are equal

But diagonals of a parallelogram are not equal whereas they are equal for rectangle

**Formula used:**

The distance between any two points (a, b, c) and (m, n, o) is given by,

Therefore,

Distance between A(1, 3, 0) and B(-5, 5, 2) is AB,

Distance between B(-5, 5, 2) and C(-9, -1, 2) is BC,

Distance between C(-9, -1, 2) and D(-3, -3, 0) is CD,

Distance between A(1, 3, 0) and D(-3, -3, 0) is AD,

Clearly,

AB = CD

BC = AD

Opposite sides are equal

Now, we will find length of diagonals

Distance between A(1, 3, 0) and C(-9, -1, 2) is AC,

Distance between B(-5, 5, 2) and D(-3, -3, 0) is BD,

Clearly,

AC BD

The diagonals are not equal, but opposite sides are equal

Thus, **Quadrilateral formed by ABCD is a parallelogram but not a rectangle**

**Hence** **Proved**

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