Diagonals of an isoseles trapezoid are perpendicular always,sometimes,or never.
What would make them perpendicular?
http://en.wikipedia.org/wiki/Isosceles_trapezoid
To determine whether the diagonals of an isosceles trapezoid are perpendicular, we need to understand the properties of an isosceles trapezoid.
An isosceles trapezoid is a quadrilateral with two parallel sides called bases (one longer and one shorter) and two non-parallel sides called legs. The legs of the trapezoid are congruent (i.e., they have the same length). Let's label the bases as BC (longer base) and AD (shorter base), and the legs as AB and CD.
To determine if the diagonals are perpendicular, we need to consider the possible cases:
1. If the isosceles trapezoid is also a rectangle:
In this case, the diagonals are always perpendicular. Since a rectangle has all right angles, both pairs of opposite sides are perpendicular, including the diagonals.
2. If the isosceles trapezoid is not a rectangle:
In this case, the diagonals are sometimes perpendicular, and sometimes not. The diagonals will be perpendicular if and only if the non-parallel sides (legs) are congruent and their midpoints coincide. If the legs are not congruent or their midpoints do not coincide, the diagonals will not be perpendicular.
To summarize, the diagonals of an isosceles trapezoid are perpendicular in the case of a rectangle, and sometimes perpendicular in non-rectangular isosceles trapezoids.