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