1. Angle Constructions

• Copying an Angle: Steps to construct an angle equal to a given angle by transferring arc measurements.
• Angle Bisector: Drawing a line that divides a given angle into two equal parts using arcs of equal radii.
• Standard Angles:
  • 60°: Built by drawing an arc and cutting it with the same radius.
  • 30°: Created by bisecting a 60° angle.
  • 90°: Constructed using arcs to find a point equidistant from two points on a line, creating a perpendicular.
  • 45°: Created by bisecting a 90° angle.
• Angle Addition: Constructing complex angles by adding or doubling given angles (e.g., x + y or 2x + y).

2. Line and Perpendicular Constructions

• Bisector of a Line Segment: Dividing a line into two equal parts. This can be done by creating equal angles at both ends or by using the perpendicular bisector method.
• Perpendicular Bisector: A line that cuts a segment at its midpoint at a 90° angle, constructed by drawing arcs from both ends of the segment with a radius greater than half its length.
• Perpendicular to a Line:
  • From a point on the line.
  • From an external point.
• Parallel Lines: Three distinct methods are provided:
  • By drawing alternate angles.
  • By drawing corresponding angles.
  • At a specific distance from the original line.

3. Construction of Quadrilaterals

The sources detail specific requirements for constructing various four-sided figures:

General Quadrilaterals

• Using four sides and one angle.
• Using three consecutive sides and two included angles.
• Using four sides and one diagonal.
• Using three sides and two diagonals.
• Using two adjacent sides and three angles.

Special Quadrilaterals

• Parallelogram: Constructed using the property that opposite sides are equal. Methods include using two sides and an included angle, two sides and a diagonal, or both diagonals and the angle between them.
• Rectangle: Constructed using properties such as all angles being 90° and equal diagonals. Methods include using two adjacent sides, one side and a diagonal, or diagonals and their intersection angle.
• Rhombus: Built on the property that all sides are equal and diagonals bisect at 90°. Methods include using one side and an angle, one side and a diagonal, or both diagonals.
• Square: The most regular construction where all sides are equal and all angles are 90°. It can be constructed given just one side or one diagonal.