taurtischan2007
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Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle?
Coordinates of rectangle ABCD: A(5,5) B(7,3) C(3,0) D(1,2)
A) Prove that segments AD and AB are congruent and parallel
B) Prove that opposite sides are congruent and that the slopes of consecutive sides are equal
C) Prove that segments BC and CD are congruent and parallel
D) Prove that opposite sides are congruent and the slopes of consecutive sides are opposite reciprocals

Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle Coordinates of rectangle ABCD A55 B73 C30 D12 A P class=

Respuesta :

olayemiolakunle65

Considering the coordinates of the vertices of rectangle ABCD, the appropriate statement that will explain the prove is that of option D. Prove that opposite sides are congruent and the slopes of consecutive sides are opposite reciprocals.

A rectangle is a quadrilateral that has opposite sides to have equal length, and the sum of its interior angles is given as [tex]360^{o}[/tex]. Thus, the coordinates of the given rectangle ensure that the required statement is unique to the rectangle.

Since opposite sides of a rectangle are equal and parallel, then options A and C are wrong. Also, the consecutive sides of the given rectangle do not have the same slope. Thus option B is not appropriate.

But, the inverse and change of the sign of the slope for each consecutive sides gives their opposite reciprocals. Therefore, the statement that is required to prove that quadrilateral ABCD is a rectangle is D.

Option D. Prove that opposite sides are congruent and the slopes of consecutive sides are opposite reciprocals.

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