Plane geometry constructions: a solved example
Draw a line AB, 90 mm long, and divide it into 3 equal parts.
Every line below was drawn and checked by Graspline's own geometry engine, by the textbook method, one step at a time with the reason for each.
The construction, step by step
Draw the line AB
AB is 90 mm long, to be divided into 3 equal parts.
Mark 3 equal divisions on a ray from A and join the last to B
From A draw a ray at a convenient angle to AB. With a compass, step off 3 equal divisions 1, 2, … 3 along it — any convenient length, here 35 mm — then join point 3 to B.
Draw parallels to mark the division points on AB
Through points 1, 2, … 2, draw lines parallel to (point 3)B. Each meets AB at a division point; by similar triangles these cut AB into 3 equal parts of 30 mm.
✓ Verified: every division point sits at an exact multiple of 30 mm from A.
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