Constructing a Quadrilateral
Let me explain the main methods for constructing quadrilaterals. These methods are used in geometric construction using a compass and straightedge.
Construction by Four Sides (Side-Side-Side-Side or SSSS Method):
- Start with four given sides
- Draw the first side AB
- Use compass to draw arcs with radii equal to two adjacent sides from points A and B
- Where these arcs intersect gives point C
- Similarly, construct the final vertex D using remaining sides
- This method has two possible solutions unless additional conditions are specified
Construction by Three Sides and Two Diagonals (SSD Method):
- Begin with three sides and two diagonals
- Draw the first diagonal
- Use compass to locate vertices using given sides as radii
- Complete the quadrilateral using remaining measurements
- This provides a unique solution
Construction by Four Sides and One Diagonal (SSSS-D Method):
- Draw the diagonal first
- Construct triangles on either side of the diagonal using the given sides
- This gives a unique quadrilateral
Construction by Four Angles and One Side (AAAA-S Method):
- Start with the given side
- Use angle construction to create rays at required angles
- Mark off remaining sides where rays intersect
- This creates a unique quadrilateral up to similarity
Construction by Four Sides and One Angle (SSSS-A Method):
- Draw first side and construct given angle
- Use compass to mark remaining sides
- Complete construction using intersections
- Generally gives a unique solution