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A trapezoid can have 4 equal sides and one right angle.
Rhombus, trapezoid, parallelogram
Any polygon with 4 or more sides can always have a right angle.
No shape does. If it has 4 sides and one pair of parallel lines it cannot have only 1 right angle, it must either have: 1) 2 right angles, 1 acute acute and 1 obtuse angle; or 2) no right angles, 2 acute angles and 2 obtuse angles; in which case it would be a trapezium (trapezoid).
A right-angled triangle can be an Isosceles Triangle, but NOT an equilateral triangle. An Isosceles triangle has two sides of equal length. They form the 90 degree (right angle). The hypotenuse is opposite the right angle, and is longer than the other two sides.