Trace a construction from step 1 and test each line against the conditions. The first line that fails is the one to report.
This lesson is part of geometric construction reasoning. It builds on comparing construction steps in two diagrams.
How do you trace a construction?
List the conditions from the question before you read the steps. Then read each step and ask, “does this line keep every condition true so far?”
Stop at the first step that does not. Every line after it is built on that mistake.
Worked example: a triangle with three given sides
The question: construct triangle ABC with AB = 70 mm, AC = 50 mm and BC = 60 mm.
A student’s steps were:
- Draw AB = 70 mm.
- With A as centre and radius 50 mm, draw an arc above AB.
- With B as centre and radius 50 mm, draw an arc to cut the first arc at C.
- Join AC and BC.
- Label the triangle and mark its sides.
Test each step against the conditions:
- Step 1: AB = 70, correct.
- Step 2: the arc places C 50 mm from A, so AC = 50, correct.
- Step 3: the arc places C 50 mm from B, but BC should be 60 mm. Inconsistent.
The first inconsistent line is the arc in step 3. Steps 4 and 5 are only wrong because C is in the wrong place.
The correct step 3 uses radius 60 mm from B. The resulting triangle has sides 70, 50 and 60, and it exists because 50 + 60 = 110 is greater than 70.
The mistake: repairing the last line
The student measures BC in the finished triangle, finds 50 mm, and extends the line to 60 mm. The sides now read 70, 50 and 60, but point C is no longer where the arcs met.
| Fix | Wrong | Right |
|---|---|---|
| What was changed | Line BC, step 4 | Arc radius, step 3 |
| Point C | Moved by eye | Found as an arc intersection |
| Condition AC = 50 | Now broken, since C moved | Holds |
Extending BC breaks AC, because C is no longer 50 mm from A. A patch at the end breaks an earlier condition, so the repair belongs at step 3.
A second trace: a tangent circle
The question asks for a circle of radius 30 mm tangent to a line L at point T. The student draws a perpendicular to L at T, marks O 30 mm from T along it, then draws the circle with radius 35 mm.
The perpendicular and the position of O are correct. The first inconsistent line is the circle. O is 30 mm from L, so a 35 mm circle crosses L at two points instead of touching it once, and it does not pass through T.
Check yourself
A student constructs a square ABCD with side 40 mm. Steps: draw AB = 40 mm; draw a perpendicular at A; mark D on it 45 mm from A; draw a perpendicular at B; mark C on it 40 mm from B; join DC. Find the first inconsistent line.
Answer
The perpendicular at A and the position of AB are correct. Marking D 45 mm from A is the first inconsistent step, because AD must equal 40 mm. Marking C correctly and joining DC do not repair it: DC would then be slanted and the figure would be a trapezium, not a square.
What to study next
Move on to checking a completed construction against the given conditions, then use the practice set.
If you want a teacher to trace your steps on your own drawings, see online one-to-one Engineering Drawing tuition.