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.