Constructions

  • Constructions are geometric figures drawn accurately using a straightedge and a compass.

  • You can construct various geometric shapes such as triangles, angles of specific degrees, perpendicular and parallel lines, etc.

  • To construct an equilateral triangle:
    1. Draw a straight line of any length using a straightedge.
    2. Use a compass and open it to the same length as the line you’ve just drawn.
    3. Set the compass at one end of the line and draw two arcs from each end to meet at a point above the line.
    4. Connect the point where the arcs meet to the ends of the original line to form an equilateral triangle.
  • Constructing perpendicular lines:
    1. Draw a line and pick a point on that line.
    2. Set the compass on that point and draw an arc cutting the line at two points.
    3. Without changing the compass width, draw arcs from each of the two points to intersect above the line.
    4. Draw a line from the original point to the point where the arcs intersect. You have now drawn a perpendicular line.
  • Constructing 60 and 120-degree angles:
    1. To construct a 60-degree angle, set the compass to a convenient radius.
    2. Draw an arc that intersects the base line.
    3. Keeping the compass wide open to the same length, draw an arc from the point where the first arc cuts the base line.
    4. Draw a line from the center of the first arc through the point where the arcs intersect. You have now drawn a 60-degree angle.
    5. To draw a 120-degree angle, reverse the process of constructing a 60-degree angle.

  • Remember: Constructions require precision. Always ensure the compass width remains unchanged throughout each individual task unless specified, and lines are sharply drawn.

  • Practice constructing these shapes and lines multiple times to improve accuracy and speed.

  • Keep in mind to understand why each step of the construction process is necessary for creating an accurate figure. It helps grasp the concept better and apply it effectively in questions.

  • Try solving a wide array of problems related to constructions to get comfortable with the concept and challenge your understanding.

  • In addition to these, understand the key terms like perpendicular bisector (line that cuts another line segment into two equal parts at 90 degrees), angle bisector (line that splits an angle into two equal angles), etc. Use these terms when writing down your construction steps. It shows clear understanding and proper mathematical style.