Regents Exam Questions - G.g.69 Quadrilaterals In The Coordinate Plane 2 Worksheet With Answers Page 5

ID: A

3 ANS:

To prove that ABCD is a parallelogram, show that both pairs of opposite sides of the parallelogram are parallel by

showing the opposite sides have the same slope:

A rectangle has four right angles. If ABCD is a rectangle, then

, and

. Lines

that are perpendicular have slopes that are the opposite and reciprocal of each other. Because

and

are not

opposite reciprocals, the consecutive sides of ABCD are not perpendicular, and ABCD is not a rectangle.

REF: 060633b

4 ANS:

. To prove that ABCD is a rhombus, show that all sides are congruent using the distance formula:

REF: 060327b

5 ANS:

(Definition of

slope).

(Parallel lines have equal slope). Quadrilateral ABCD is a parallelogram (Definition of

parallelogram).

(Definition of

distance).

is not congruent to

(Congruent lines have equal distance). ABCD is not a rhombus (A rhombus

has four equal sides).

REF: 061031b

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