Module 10 coordinate proof using slope and distance answers is quadrilateral abcd a parallelogram? explain how you know.

Yes, both pairs of opposite sides are parallel

Step-by-step explanation:

The complete question is shown in the picture attached.

The 4 sides of the parallelogram are formed by segments AB, BC, CD and DA. We need to prove that segments AB and CD, and  BC and DA are parallel between them. To do that we calculate their slopes.

slope of segment AB: (6-4)/(3-2) = 2

slope of segment CD: (6-4)/(8-7) = 2

Then, segments AB and CD are parallel

slope of segment BC: (6-6)/(8-3) = 0

slope of segment DA: (4-4)/(7-2) = 0

Then, segments BC and DA are parallel

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

95.03 is the answer. hope this !