Key Points

A compass is a fundamental tool for drawing circles and arcs. The distance set between the metal tip (center) and the pencil tip defines the radius of the circle.

A circle is a collection of all points that are at a fixed distance from a central point. The central point is called the center, and the fixed distance is called the radius.

A rectangle is a four-sided figure with two main properties: 1) Its opposite sides are equal in length. 2) All four of its interior angles are right angles, each measuring $90^\circ$.

A square is a special type of rectangle where all four sides are equal in length. Like a rectangle, all its interior angles are right angles ($90^\circ$).

When naming a polygon like a rectangle ABCD, the vertices must be listed in a consecutive order, either clockwise or counter-clockwise. For example, ACBD is an incorrect name.

To construct a square of side length $s$, draw a line segment of length $s$. Then, construct perpendicular lines of the same length $s$ at both endpoints and join the new endpoints to complete the figure.

To construct a rectangle with length $l$ and breadth $b$, draw a base of length $l$. At its endpoints, construct perpendiculars of length $b$. Join the tops of these perpendiculars to form the rectangle.

To locate a point that is at distance $r_1$ from point A and distance $r_2$ from point B, draw an arc of radius $r_1$ from A and an arc of radius $r_2$ from B. The intersection of these arcs gives the required point.

The diagonals of a rectangle, which are lines connecting opposite corners, are always equal in length. This property can be used to check the accuracy of a constructed rectangle.

The diagonals of a square are not only equal in length but also divide each corner angle into two equal parts of $45^\circ$ each.

To construct a rectangle given one side $s$ and a diagonal $d$, first draw the side. Construct a perpendicular line at one end. From the other end of the side, use a compass to draw an arc of radius $d$ that intersects the perpendicular line, locating the third vertex.

Before beginning any geometric construction, it is always helpful to draw a rough, freehand sketch of the final figure. This helps in planning the order of steps and understanding the relationships between the parts.