Well, honey, a rhombus is a special type of quadrilateral with all sides equal, while an isosceles trapezoid has at least one pair of parallel sides. So, technically speaking, a rhombus can be considered an isosceles trapezoid if you squint your eyes and tilt your head a bit, but let's not get too carried away with geometry gymnastics now.
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Yes, an isosceles trapezoid is symmetrical.
A quadrilateral may have all 4 angles different if it is not a square, rectangle, rhombus, rhomboid, rectangular trapezoid, isosceles trapezoid, or parallellogram.
If you extend the two legs of an isosceles trapezoid until they intersect, you get an isosceles triangle.
it depends general: quadrilateral, polygon only some: trapezoid, parallelogram, rhombus, square, isosceles trapezoid, etc. (i'm pretty sure there's more)
No. It can be but need not be.