Question

Complete the proof to show that ABCD is a parallelogram. BCllAD and CDllBA because the___________. therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

A.) links of a consecutive sides are not equal
B.) slopes of opposite sides are equal
C.) lengths of opposite sides are equal
D.) slopes of consecutive sides are not equal

Answer 1

ABCD is a parallelogram.

Step-by-step explanation:

Given :- coordinates of A = (-2,-2) = (x1,y1)

coordinates of B = (-3,4) = (x2,y2)

coordinates of C = (2,2) = (x3,y3)

coordinates of D = (3,-4) = (x4,y4)

To prove :- ABCD is a parallelogram

Proof :- slope of AB is y2-y1 / x2-x1

= 4-(-2) / -3-(-2)

= (4+2)/-3+2

= 6/-1

= -6

Slope of BC is y3-y2/x3-x2

= (2-4)/(2-(-3))

= -2/(2+3)

= -2/5

slope of CD = y4-y3/x4-x3

= (-4-2)/(3-2)

= -6/1

= -6

slope of AD= y4-y1 /x4-x1

= -4-(-2)/3-(-2)

= (-4+2)/(3+2)

= -2/5

now, slope of AB = slope of CD

and slope of BC = slope of AD

hence, ABCD is a parallelogram

and AB║CD and BC║AD because slopes of opposite sides are equal

Answer 2

Answer:

The answer is C

Step-by-step explanation: I got it right