Complete the proof to show that ABCD is a parallelogram. On a coordinate plane, quadrilateral A B C D is shown. Point A is at (n
egative 2, negative 2), point B is at (negative 3, 4), point C is at (2, 2), and point D is at (3, negative 4). The slope of Line segment B C is StartFraction 4 minus 2 Over negative 3 minus 2 EndFraction = negative two-fifths The slope of Line segment A D is StartFraction negative 4 minus (negative 2) Over 3 minus (negative 2) EndFraction = StartFraction negative 4 + 2 Over 3 + 2 EndFraction = negative two-fifths The slope of Line segment C D is StartFraction 2 minus (negative 4) Over 2 minus 3 EndFraction = StartFraction 2 + 4 Over 2 minus 3 EndFraction = StartFraction 6 Over negative 1 EndFraction = negative 6 The slope of Line segment B A is StartFraction 4 minus (negative 2) Over negative 3 minus (negative 2) EndFraction = StartFraction 4 + 2 Over negative 3 + 2 EndFraction = StartFraction 6 Over negative 1 EndFraction = negative 6 and because the ________________________________. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel. lengths of consecutive sides are not equal slopes of opposite sides are equal lengths of opposite sides are equal slopes of consecutive sides are not equal
2 answers:
Answer: slopes of opposite sides are equal
Step-by-step explanation:
In the given figure we have a quadrilateral ABCD with A (-2,-2) , B(-3,4), C(2,2)
and D(3,-4).
We know that when the slope of two lines are equal then they are parallel.
In the given figure, Slope of BC= Slope of AD =
⇒ BC and AD are parallel .
Also, Slope of CD= Slope of BA =-6
⇒ CD and BA are parallel .
Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.
Hence, the correct reason for the given space = "slopes of opposite sides are equal"
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