Constructing a Triangle | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What are SSS Triangle constructions?

• SSS stands for side, side, side.
• In mathematics, a construction refers to an accurate drawing typically using tools like a ruler, protractor, and/or compasses.
  • An SSS triangle construction involves accurately drawing a triangle when only the lengths of its three sides are provided.
  • This task can be more challenging than it appears, especially without the proper tools.

How to Construct an SSS Triangle?

• When given all three sides of a triangle, you will need a pencil, ruler, and compasses.
• Step 1:
  • Use the ruler to draw the longest side as a horizontal base near the bottom of the given space.
  • Measure accurately and label its length (with units) below it.
• Step 2:
  • Measure with the ruler, then set the compasses to the length of one of the remaining sides.
  • Keeping this length, place the compass point at one end of the horizontal line and draw an arc above it.
• Step 3:
  • Measure with the ruler again, then set the compasses to the length of the third side.
  • Keeping this length, place the compass point at the other end of the horizontal line and draw another arc, ensuring it crosses the first arc.
• Step 4:
  • Use the ruler to draw straight lines from each end of the horizontal line to the intersection point of the arcs.
• Step 5:
  • Check with the ruler that the two new lines match the given lengths exactly.
  • Once confirmed, label the lines.
• Do not erase the arcs, as they are needed for verification.
• If the triangle is named (e.g., triangle ABC), label each vertex accordingly.