Michael and Jane want to build a kite with four equal sides. They know that KT and TE are eight inches which makes point T the midpoint of (KE). Describe how Michael and Jane can be absolutely certain that KI, IE, ES, and KS are all the same lengths.

We see from the figure that K and E are equidistant from T. To be absolutely certain that KI, IE, ES, and KS are all the same lengths the diagonals must bisect each other perpendicularly at 90 degrees for the given figure to be a rhombus. A rhombus is a parallelogram in which all sides are equal.

If we look at the figure more carefully then we find that there are four triangles. Of the which the two sides KE and TE of the triangles are equal. Also the diagonal indicates that they both have a 90 degrees angle. Hence the two triangles KST and EST are equal.

To prove that triangle KEI is equal to Triangle KES.

Both have one line common which equal to both.

Both have a mid point T on the common line which divides the both bigger triangles into smaller triangles making 90 degrees angle. Hence the angles

KEI and KSE are of 90 degrees which are also opposite.

The angles SKT and IKT and angles IET & SET are equal and opposite angles. Thus both the triangles KEI and triangle KES are equal and opposite having equal and opposite sides.