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

answer: check all that apply, where the options?

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!