WILL GIVE BRAINLIEST! Prove that a quadrilateral ABCD with vertices A(–1, –2), B( 2, –5), C(1, –2), and D( –2, 1) is a parallelogram. Find the point of intersection of the diagonals of parallelogram ABCD. Provide your complete solutions and proofs in your paper homework and enter the numeric answers online.

Step-by-step explanation:

To prove a quadrilateral a parallelogram we prove,

1). Length of opposite sides are equal.

2). Slopes of the opposite sides are same.

Length of AB =

                      =

                      =

Length of BC =

                      =

Length of CD =

                      =

Length of AD =

                      =

Therefore, AB = CD and BC = AD (Opposite sides are equal in length)

Slope of AB =

                    =

                    = -1

Slope of BC =

                    = -3

Slope of CD =

                    = -1

Slope of AD =

                    = -3

Slope of AB = slope of CD and slope of BC = slope AD

Therefore, AB║CD and BC║AD

Hence ABCD is a parallelogram

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)

-6 is the correct option from the above given options