Not usually.
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No.
perpendicular
Not usually.
The diagonals of an isosceles trapezoid are equal in lengths but are not perpendicular to each other at right angles.
Oh, dude, no way! Diagonals of a trapezoid are not necessarily perpendicular. It's like saying all cats are secretly plotting to take over the world - just because they're diagonal doesn't mean they're perpendicular, you know what I mean? So yeah, diagonals of a trapezoid can be any ol' angle they want, they don't have to be all right angles and stuff.