Construct an equilateral triangle or regular hexagon
Key Notes :
✏️ Basic Tools Needed
- 📏 Ruler (scale) – to draw straight lines
- 🧭 Compass – to draw arcs and circles
- ✏️ Pencil – for neat construction
🔺 Constructing an Equilateral Triangle
An equilateral triangle has:
- All three sides equal
- All three angles = 60°
🪜 Steps:
- Draw a line segment AB of any given length.
- With A as centre, draw an arc with radius AB.
- With B as centre, draw another arc with the same radius.
- Let the arcs intersect at C.
- Join AC and BC.
✅ △ABC is an equilateral triangle.
⬡ Constructing a Regular Hexagon
A regular hexagon has:
- 6 equal sides
- 6 equal angles (each = 120°)
🪜 Steps:
- Draw a circle with centre O and any radius.
- Mark a point A on the circle.
- With A as centre and same radius, cut the circle at B.
- Repeat this step to get points C, D, E, F on the circle.
- Join A–B–C–D–E–F–A.
✅ ABCDEF is a regular hexagon.
💡 Important Observations
- The side of a regular hexagon = radius of the circle.
- A regular hexagon can be divided into 6 equilateral triangles.
- Accuracy in compass opening is very important.
🧠 Quick Tips for Students
- Do not change the compass width during construction.
- Draw light arcs and darken final lines.
- Always label points clearly.
Learn with an example
🌀 The diagram below shows a nearly completed construction of an equilateral triangle with side AB. Complete the construction.
Part of the construction was done for you. Here are the steps to create this part of the construction.
Start with the objects in the diagram below.
Draw a circle with radius AB centred at A.
Draw a circle with radius AB centred at B.
Mark a point where ⨀A and ⨀B intersect. Call it C.
Complete the construction.
To complete the construction of an equilateral triangle with side AB, carry out the following steps:
- Draw the segment between A and C.
Draw the segment between B and C.
Since B and C are both on ⨀A, AB=AC. Since A and C are both on ⨀B, AB=BC.
Since AB=BC=AC, △ABC is an equilateral triangle.
🌀 The diagram below shows a nearly completed construction of an equilateral triangle with side AB . Complete the
construction.
Part of the construction was done for you. Here are the steps to create this part of the construction.
Start with the objects in the diagram below.
Draw a circle with radius AB centred at A.
Draw a circle with radius AB centred at B.
Mark a point where ⨀A and ⨀B intersect. Call it C.
Complete the construction.
To complete the construction of an equilateral triangle with side AB, carry out the following steps:
- Draw the segment between A and C.
Draw the segment between B and C.
Since B and C are both on ⨀A, AB=AC. Since A and C are both on ⨀B, AB=BC.
Since AB=BC=AC, △ABC is an equilateral triangle.
🌀 The diagram below shows a nearly completed construction of an equilateral triangle with side AB. Complete the construction.
Part of the construction was done for you. Here are the steps to create this part of the construction.
Start with the objects in the diagram below.
Draw a circle with radius AB centred at A.
Draw a circle with radius AB centred at B.
Mark a point where ⨀A and ⨀B intersect. Call it C.
Complete the construction.
To complete the construction of an equilateral triangle with side AB, carry out the following steps:
- Draw the segment between A and C.
Draw the segment between B and C.
Since B and C are both on ⨀A, AB=AC. Since A and C are both on ⨀B, AB=BC.
Since AB=BC=AC, △ABC is an equilateral triangle.
let`s practice!
