GCSE Maths Practice: loci-and-constructions

Question 8 of 10

This question introduces constructing an equilateral triangle using a compass and ruler.

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\( \begin{array}{l}\text{Describe how to construct an equilateral triangle with sides 5 cm long.}\end{array} \)

Choose one option:

Draw one side first, then arcs from both endpoints with radius equal to the side; connect intersections.

To construct an equilateral triangle with sides of 5 cm, students use a compass to draw arcs from two endpoints of a base side. The radius of each arc equals the side length, ensuring that each vertex is exactly 5 cm from the others. The intersection of the arcs locates the third vertex. Connecting this vertex to the base completes the triangle. Practising this method develops geometric construction skills, spatial reasoning, and precision with compass and ruler. Understanding equilateral triangles is foundational for loci, triangle properties, and more advanced constructions. Students should practise drawing multiple examples to internalise the method and ensure accuracy.