Triangle ADC is formed by joining the coordinates A(2,6), C(4,0) and D(0,0). Another $Δ$ BCD is formed by joining the coordinates B(6,6), C(4,0) and D(0,0). Line y=6 and y=0 is parallel to each other. The points C(4,0) and D(0,0) lies on y = 0. The points A(2,6) and B(6,6) lies on line y=6. ABCD forms a quadrilateral. Which of the following is correct?

Quadrilateral ABCD is rectangle.

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Quadrilateral ABCD is square.

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Quadrilateral ABCD is parallelogram.

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Quadrilateral ABCD is rhombus.

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Solution

The correct option is C
Quadrilateral ABCD is parallelogram.

AB is joined. Since y = 6 and y = 0 are parallel to each other; AD and BC are parallel to each other.
Also AD = BC, AB = CD.

In a quadrilateral ABCD, if opposite sides are parallel and equal then ABCD is a parallelogram.

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Similar questions

$△$ ADC is formed by joining the coordinates A(2,6), C(4,0) and D(0,0). Another $△$ BCD is formed by joining the coordinates B(6,6), C(4,0) and D(0,0). BD intersects AC at O. What is the relation between the areas of $△$ AOD and $△$ BOC?

Q. The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rhombus, if
(a) ABCD is a Parallelogram
(b) ABCD is rhombus
(c) diagonals of ABCD are equal
(4) diagonals of ABCD are perpendicular to each other.

Points A(1,0), B(5,0), C(7,6) and D(3,6) are joined to form a quadrilateral ABCD. Point B(5,0) is joined with E(5,6) and A(1,0) is joined with F(1,6). Quadrilateral ABEF is now formed. What is the relation between the perimeter of the quadrilateral ABCD and quadrilateral ABEF?

Q. The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rectangle, if
(a) ABCD is a Parallelogram
(b) ABCD is rectangle
(c) diagonals of ABCD are equal
(d) diagonals of ABCD are perpendicular to each other.

The quadrilateral formed by joining the mid-points of consecutive sides of a rectangle ABCD, taken in order, is a rhombus.

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The correct option is C Quadrilateral ABCD is parallelogram. AB is joined. Since y = 6 and y = 0 are parallel to each other; AD and BC are parallel to each other. Also AD = BC, AB = CD. In a quadrilateral ABCD, if opposite sides are parallel and equal then ABCD is a parallelogram.

The correct option is C
Quadrilateral ABCD is parallelogram.

AB is joined. Since y = 6 and y = 0 are parallel to each other; AD and BC are parallel to each other.
Also AD = BC, AB = CD.

In a quadrilateral ABCD, if opposite sides are parallel and equal then ABCD is a parallelogram.