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Step-by-step Answer
PAGE: 352SET: ExercisesPROBLEM: 6
Please look in your text book for this problem Statement

Explore:   Plot the vertices on a coordinate plane.

Plan:

If the diagonals are perpendicular, then ABCD is either a rhombus or a square.

The diagonals of a rectangle are congruent. If the diagonals are congruent and perpendicular, then ABCD is a square.

Graph of the quadrilateral having vertices M(0,3),N(-3,0),P(0,-3),Q(3,0) Solve:

Use the Distance Formula to compare the lengths of the diagonals.

The distance formula is  .

   (Substitute )

                         (Simplify)

     (Substitute )

                       (Simplify)

Use slope to determine whether the diagonals are perpendicular.

The slope formula is .

Slope of          (Substitute )

                

Slope of             (Substitute )

                

Since the slope of is the negative reciprocal of the slope of , the diagonals are perpendicular. and   have the same measure, so the diagonals are congruent. ABCD is a rhombus, a rectangle, and a square. ABCD is a rhombus, a rectangle, and a square.



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