This is false. In 18th and 19th centuries, mathematicians have actually proven that these structures are indeed impossible to construct. These structures are shown in the attached picture.
The first one is trisecting an angle. Given an angle, constructing an angle 1/3 as the large angle is impossible to construct as proven by Gauss in 1800 and Wantzel in 1837. It was proven through the trial of trisecting a 60° angle using only an unmarked ruler and a compass.
The second problem is the squaring of a circle. It is impossible to construct a square that has the same area as a circle. This could only be true if the ratio of the side of the square to the radius is equal to π. Since this is an irrational number, you cannot construct this in planar geometry as proven by Lindemann in 1882.
The last construction is doubling the cube. It is impossible to double the volume of the cube. Suppose the square has a side with 1 unit then its volume is 1 cubic unit. In order to make the volume to 2 cubic units, the side of the new cube should be √2. Since this is an irrational number, you cannot construct this in planar geometry using only an unmarked ruler or compass. This was proven by Wantzel in 1837.