 # Doubling a Line Segment Using a Right Angle

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This Demonstration shows how to double a line segment using only a right angle (e.g. a carpenter's square, a try square or an iron square). No compass is needed.

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Step 1: draw a ray Step 2: draw a straight line through Step 3: let be the intersection of and a perpendicular through Step 4: let be the intersection of a perpendicular through and the extension of Step 5: let be the intersection of the line through perpendicular to and the line through perpendicular to Step 6: let be the perpendicular projection of to Step 7: let be the perpendicular projection of to Then is twice as long as .

Verification

The triangles and are congruent, and the quadrilateral is a rectangle. So .

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Contributed by: Izidor Hafner (September 2017)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

Axioms for a ruler:

The line segment between two points can be constructed.

The infinite straight line through two points can be constructed.

A half-infinite ray from a given point through another point can be constructed.

Additional axioms for a right angle:

Through a given point, a straight line perpendicular to a given straight line can be constructed.

Given a line segment and a figure , it is possible to decide whether contains a point from which subtends a right angle. If such a point exists, it is possible to construct this point.

The last axiom is not used in this Demonstration.

Reference

 B. I. Argunov and M. B. Balk, Elementary Geometry (in Russian), Moscow: Prosveščenie, 1966 pp. 268–269, pp. 332.

## Permanent Citation

Izidor Hafner

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