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Yes
no
No.
No. An isosceles trapezium (isosceles triangle with its apex removed) would have congruent diagonals but it is not a parallelogram.
Yes. Any triangle will tessellate.
Yes
Yes under certain dimensional conditions.
no
no
No - a triangle by definition has 3 sides. A parallelogram has 4.
yes you can tessellate a triangle and a pentagon together.
There is no such thing as a regular isosceles triangle. The only regular triangle is an equilateral triangle. Having said that, any triangle will produce regular tessellation.
isosceles triangle
If their shapes are suitably matched they can tessellate together.
A parallelogram is two triangle together.
No.
No * * * * * Yes it can: and in many ways. One possible way is to add a right isosceles triangle to each side of the square (with the hypotenuse along the square) to make it a larger square!