Suppose, we have to draw a quadrilateral. The length of three given sides are 'a' units, 'b' units and 'c' units. The measure of two given angles is $\alpha$ and $\beta$. 
The first step is to construct a line segment AB = 'a' units. Taking AB as the base, we construct a line making an angle $\alpha$ with the line segment AB. We cut the line by an arc of length 'b' units taking B as center and mark point where arc cuts the line as C.
Taking BC as the base, we construct a line making an angle $\beta$ with the line segment BC. We cut the line by an arc of length 'c' units taking C as center and mark point where arc cuts the line as D. 
The final step is to join A and D to complete the quadrilateral ABCD.

As all the sides are equal and all the angles measure 90 degrees in a square, the given information is enough to construct a square.

A Kite is a quadrilateral in which both the adjacent sides are equal to each other. Also, one of the opposite angles is equal. Therefore, to construct a Kite, length of two unequal sides must be given. Also, the length of the diagonal or the measure of any one of the angles must be given. 

3 sides and 2 diagonals of a quadrilateral is known. This information is enough to construct a quadrilateral. Thus, a protractor is not necessary for the construction because no angles are measured or drawn during construction.

To construct a quadrilateral, we need to construct two triangles. As, both the diagonals are known, we can construct any of the two triangles first. Thus, there are two ways to start this construction.

To make the two line segments meet, arcs are drawn and their intersection point is found. A compass is hence used.