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Yes, an isosceles trapezoid can have at least one right angle. In such a trapezoid, the non-parallel sides are equal in length, and if one of the angles between a base and a non-parallel side is a right angle, the trapezoid will still maintain its isosceles properties. This configuration results in a trapezoid that is both isosceles and contains a right angle.
Depending how you halve it can be a right angle triangle or an isosceles trapezoid
An isosceles trapezoid would fit the given description
The diagonals of an isosceles trapezoid are equal in lengths but are not perpendicular to each other at right angles.