Sonta Murray

6/5/03

INVESTIGATION 4

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QUESTION:

A diagonal of a polygon is created when two non-consecutive vertices are connected by a segment. Place the mouse over the picture below for an illustration.

 

In convex quadrilaterals, the diagonals can:

 

    * be non-congruent

    * be congruent

    * bisect each other

    * meet at right angles

 

Find all of the possible combinations of diagonals that can occur and construct the quadrilateral that they define.

 

 

Pick a point on the line, then drag.  You will see the different quadrilaterals that are formed.(Go to the gsp document)

 

When the diagonals are non-congruent and /or bisect each other, quadrilaterals such as trapezoids, rectangles, and parallelograms will be formed.

 

When the diagonals are congruent and/or meet at right angles, a square or a rhombus is formed.

 

Wow!!