Line t contains side AB of the triangle.
Choice (E) can occur when a line divides an isosceles right triangle into two smaller identical
isosceles right triangles. This is shown in this figure.
Line t divides isosceles right triangle ABC into smaller identical isosceles right triangles ABD
and BCD.
It is also true that if the vertex opposite the hypotenuse of any right triangle is connected to
the midpoint of the hypotenuse, the right triangle is divided into two isosceles triangles.
Thus, a line containing the line segment whose endpoints are (1) the vertex of the right
triangle that is opposite the hypotenuse of a right triangle and (2) the midpoint of the
hypotenuse divides the right triangle into two isosceles triangles. However, if the original
right triangle is not an isosceles right triangle, the two isosceles triangles formed from the
original right triangle are not identical.