A finished construction is checked by matching each stated condition with the step that created it. If a condition has no matching step, the construction is not finished.
This lesson belongs to geometric construction reasoning. If a check fails, use finding the first inconsistent line.
What does a condition checklist look like?
Make a three-column list: the condition, the step that enforces it, and a yes or no. A condition with a blank in the middle column is the one to fix.
The checklist takes about a minute, and it shows a missing step before a marker does.
Worked example: a regular hexagon in a circle
The question: draw a regular hexagon inside a circle of radius 40 mm.
The construction: draw the circle with centre O. Keep the compass at 40 mm, put the point on the circle at A, and mark arcs on the circle at B, C, D, E and F in turn. Join the six points.
| Condition | Evidence | Met? |
|---|---|---|
| Six vertices on the circle | A to F all marked on the circle | Yes |
| All sides equal | Each side is a chord from an arc of radius 40 mm, so equals OA | Yes |
| Side length | Each side = 40 mm | Yes |
| Closed after six steps | Six 60° arcs make 360° | Yes |
The reasoning: triangle OAB has OA = OB = 40 and AB = 40, so it is equilateral and angle AOB = 60°. Six of them fill 360°, so the last mark lands on A again. If it does not, the compass radius moved during the construction.
An extra numerical check: the distance from A to its opposite vertex D is 2 × 40 = 80 mm, which equals the circle’s diameter.
Worked example: a tangent line to a circle
The question: draw a tangent to a circle of centre O and radius 30 mm at point P on the circle.
The construction: join OP, extend it, then draw a line through P perpendicular to OP.
| Condition | Evidence | Met? |
|---|---|---|
| Line passes through P | Drawn through P | Yes |
| Line touches the circle only once | Perpendicular to radius OP at P | Yes |
| Radius is 30 mm | OP drawn as radius | Yes |
The key fact is that a tangent meets the radius at right angles at the point of contact. Without that step, the line might cut the circle twice.
The mistake: checking the look of the drawing
A student checks the hexagon by looking at the shape and saying it “looks regular”. The compass slipped to 42 mm for the last two arcs, so the final side is shorter than the others, but the error is too small to see.
| Method | Wrong | Right |
|---|---|---|
| Check | Looks regular | Every arc used 40 mm |
| Evidence | Appearance | Steps that force equal sides |
| Result | Error passes | Slip is found |
Check yourself
A question asks for a triangle ABC with AB = 60 mm, angle at A = 60° and AC = 60 mm. The student drew AB, used a protractor for 60° at A, and marked C 60 mm along it. Make a condition checklist and say whether the construction is complete. What is BC?
Answer
Conditions: AB = 60 (drawn), angle A = 60° (protractor), AC = 60 (marked). All three have evidence, so the construction is complete. Since AB = AC and the angle between them is 60°, the triangle is equilateral, so BC = 60 mm.
What to study next
Test yourself on all four lessons with the construction reasoning practice set.
If you want a teacher to go through your checklist on a real construction, see online one-to-one Engineering Drawing tuition.