Perpendicular and parallel through a point, and constructing from data
From a point outside a line, construct a perpendicular and a parallel, then build a rhombus and an isosceles triangle with the compasses by analysing the problem first.
- Iran: grade 10
- Palestine: grade 10
- Russia: grade 7
Guide
This studio continues the ruler-and-compass work of Iran's Grade 10 geometry 1 (chapter 1, lesson 1).
Perpendicular from a point outside a line: draw a circle centred on the point that cuts the line twice. The point is the same distance from both crossings, so it lies on their perpendicular bisector. That bisector is the perpendicular we want.
Parallel through a point: build a rhombus with one side on the line and the opposite corner at the point. Opposite sides of a rhombus are parallel.
Before drawing, analyse the problem: pretend the figure is already drawn. What do you know? Each corner is a known distance from two others, so it lies where two circles cross.