Is it possible to draw parallelogram so that all sides are equal to one of its diagonals? if it is, what would the angles of the parallelogram be?

yes it is.

diagonals of parallelogram bisect each other so if the diagonals are of equal length then they bisect each other and length of each bisect is equal. so the angle made by these bisects with any sides should be equal ( it is a theorem of geometry ) if all such angles are equal then the length all the sides with which these angles are made should of equal.now if all the sides has same length then it is rhombus and here all angles have same values that is x+x+x+x=360; x=90

so it is proved that it is a rectangle.

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: