Given only a line segment there are numerous steps that need to be taken to construct a diamond. Recall a diamond is a parallelogram with four equilateral sides where the diagonals are vertical and horizontal.

The first step in constructing a diamond would be to calculate the length of the line segment . After the length is known then the slope can be found and from there, each of the connecting lines can be drawn. 

Therefore, the correct answer is,

"Calculate the length of ."

To determine which image illustrates a triangle that is inscribed in a circle, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a triangle inscribed in a circle means the triangle will be drawn inside of a circle.

The image that illustrates this is as followed.

To determine which image illustrates a rectangle that is inscribed in a circle, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a rectangle inscribed in a circle means the rectangle will be drawn inside of a circle.

The image that illustrates this is as followed.

To determine which image illustrates a circle that is inscribed in a rectangle, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a circle inscribed in a rectangle means the circle will be drawn inside of a rectangle.

The image that illustrates this is as followed.

To determine which image illustrates a circle that is inscribed in a triangle, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a circle inscribed in a triangle means the circle will be drawn inside of a triangle.

The image that illustrates this is as followed.

To determine which image illustrates a pentagon that is inscribed in a circle, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a pentagon inscribed in a circle means the pentagon will be drawn inside of a circle.

The image that illustrates this is as followed.

To determine which image illustrates a circle that is inscribed in a pentagon, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a circle inscribed in a pentagon means the circle will be drawn inside of a pentagon.

The image that illustrates this is as followed.

First understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, a rectangle inscribed in a circle means the rectangle will be drawn inside of a circle. 

From here the following image can be constructed.

The diameter of the circle is any and all straight lines that cut the circle in half. Since the rectangle is inscribed in that circle and all corners touch the circle then the diameter of the circle is equivalent to the length of the rectangle's diagonal.

To determine whether this particular statement is true or false, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, for any object to be inscribed in a circle that means all points of that object must also be inside the circle.

Thus the statement, "For an object to be inscribed in a circle only one of its points must lie within the circle." is false.

To determine whether this particular statement is true or false, first understand what the term "inscribed" means.

"Inscribed" means to draw inside of. Therefore, any and all polygons can be inscribed in a circle and circles can be inscribed in all polygons.

Thus, the statement, "Polygons can be both inscribed inside a circle and have circles inscribed inside of them." is true.