Diagonals in Quadrilaterals

By:  Danielle Habeeb


A diagonal of a polygon is created when two non-consecutive vertices are connected by a segment.



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.


First I created a trapezoid.   Then, I drew the diagonals from each of the vertices.  I began investigated the measures of each of the angles and the measures of the length of the diagonals.  I found that the opposite angles were congruent and that the segments were non-congruent.


Next, I created a square.  Again, I drew the diagonals from each of the vertices.  I also investigated ay measuring the angles and the segments.  I found that the diagonals were congruent, all diagonals meet at right angles, the diagonals bisect one another, and they are perpendicular.

The next figure I created was a kite figure.  I drew the diagonals from vertex to vertex.  I found that it created 2 sets of congruent triangles. I also observed that one diagonal was a perpendicular bisector of the other.  The interior angles measured 90 degrees.



For the fourth figure, I drew a rectangle.  I constructed my diagonals.  I found that the segments were congruent, opposite interior angles were congruent, and all triangles are congruent.


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