To compare two constructions, line up their steps and find the first row that differs. Then decide which version enforces the condition the question asks for.
This lesson belongs to geometric construction reasoning. It follows on from explaining a construction using its constraints.
How do you set up a fair comparison?
Write the steps of Diagram A and Diagram B in two columns. Mark the conditions the question requires, for example “all three sides 50 mm”.
Read down row by row. The first row where the columns differ is usually the only one you must analyse, because later rows follow from it.
Worked example: two ways to draw an equilateral triangle
The question asks for an equilateral triangle with side 50 mm on base AB.
| Step | Diagram A | Diagram B |
|---|---|---|
| 1 | Draw AB = 50 mm | Draw AB = 50 mm |
| 2 | Compass to 50 mm, arc from A above AB | Compass to 50 mm, arc from A above AB |
| 3 | Compass stays at 50 mm, arc from B | Compass to 45 mm, arc from B |
| 4 | Arcs meet at C, join AC and BC | Arcs meet at C, join AC and BC |
The first difference is step 3. In Diagram A, AC = 50 mm and BC = 50 mm, and AB = 50 mm, so all three sides are equal and the triangle is equilateral.
In Diagram B, AC = 50 mm but BC = 45 mm, while AB = 50 mm. The triangle is isosceles with AB = AC, not equilateral. Its angle at A is not 60°, so it fails the condition.
Worked example: a perpendicular at the end of a line
The second pair builds a right angle at point P on a line. Diagram A draws arcs from P on both sides at equal radius, then bisects between them. Diagram B sets the set square to one side of P and draws along it without checking the edge.
The first difference is that A enforces equal distances from P, so its line is the perpendicular bisector of the segment between the marks. B relies on the set square being aligned, which the diagram does not show. A has a geometric reason. B has none unless the alignment is stated.
The mistake: judging by the final picture
A student compares the two triangles, sees that both have a peak and a base, and says both are correct. The final pictures look alike on a small screen.
| Judged by | Wrong | Right |
|---|---|---|
| Method | Final shape | First differing step |
| Side BC | Not checked | 45 mm against 50 mm required |
| Conclusion | Both correct | Only A is equilateral |
The condition lives in the steps, not in the finished picture.
Check yourself
Diagram X bisects an angle by drawing an arc from the vertex, then two arcs of the same radius from the two points where it cuts the arms. Diagram Y draws the two second arcs with different radii. Which one gives the angle bisector, and why?
Answer
Diagram X does. The two arm points are equally far from the vertex, and the equal-radius arcs from them meet at a point equally far from both arm points, so the line from the vertex to that point splits the angle into two equal parts. In Diagram Y the intersection is not equally far from the arm points, so the line does not bisect the angle.
What to study next
Practise spotting where a construction goes wrong with identifying the first inconsistent line, then try the practice set.
If you want a teacher to pair your own diagrams and discuss which meets the conditions, see online one-to-one Engineering Drawing tuition.