Verify that parallelogram abcd with me asap! i’m in a dead ! !

Its diagonals are perpendicular, then it is a rhombus

Step-by-step explanation:

* Lets revise the properties of the parallelogram and the rhombus

- In the parallelogram each two opposite sides are parallel

- In the parallelogram each two opposite sides are equal in length

- In the parallelogram the diagonals bisect each other

- In the rhombus each two opposite sides are parallel

- In the rhombus all the sides are equal in length

- In The rhombus the diagonals are perpendicular to each other

- Parallelogram is a rhombus if two adjacent sides are equal in length

- Parallelogram is a rhombus if its two diagonals are perpendicular

* Now lets solve the problem

∵ The vertices of the parallelogram are

   A(-3 , 2) , B(-2 , 6) , C (2 , 7) , D (1 , 3)

- The slope of the line which passes through points (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

* lets find the slopes of the sides and the diagonals

∵ The slope of AB = (6 - 2)/(-2 - -3) = 4/1 = 4

∵ The slope of BC = (7 - 6)/(2 - -2) = 1/4 = 1/4

∵ The slope of CD = (3 - 7)/(1 - 2) = -4/-1 = 4

∵ The slope of DA = (2 - 3)/(-3 - 1) = -1/-4 = 1/4

- The product of the slopes of the perpendicular line is -1

∵ AB and BC are two adjacent sides and the product of their slopes

  = 4 × 1/4 = 1 ≠ -1

∴ AB and BC are not perpendicular

∴ The parallelogram can not be a rectangle

- Lets check the slopes of the diagonals

∵ The diagonals of the parallelogram are AC and BD

∵ The slope of AC = (7 - 2)/(2 - -3) = 5/5 = 1

∵ The slope of BD = (3 - 6)/(1 - -2) = -3/3 = -1

∵ The product of the slopes of AC and BD = 1 × -1 = -1

∴ AC and BD are perpendicular

∴ ABCD is a rhombus

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step-by-step explanation: