# Doubling a Line Segment Using a Right Angle

Doubling a Line Segment Using a Right Angle

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.

AB

Step 1: draw a ray

AB

Step 2: draw a straight line through

a

A

Step 3: let be the intersection of and a perpendicular through

C

a

B

Step 4: let be the intersection of a perpendicular through and the extension of

D

A

CB

Step 5: let be the intersection of the line through perpendicular to and the line through perpendicular to

E

C

AC

D

AD

Step 6: let be the perpendicular projection of to

F

E

CD

Step 7: let be the perpendicular projection of to

G

E

AB

Then is twice as long as .

AG

AB

Verification

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

ADC

ECD

BGEF

AB=FE=BG