Basic Constructions
Constructing Perpendicular Lines
I. From a point to a line
II. Perpendicular Bisector
Given a line l and a point P not on l, construct a line through P,
perpendicular to line l.
Step 1: Open your compass so that
when you place the point of the compass
at P the compass extends past line l, and
make an arc that intersects line l in two
places. Label these points A and B.
P
Put compass
PutPut
compass
compasspoint here
point
here
point
here
B
A
C
l
Step 2: Place the point of your compass
at point A and open your compass so that
it extends close to B and make an arc
below line l.
Step 3: Using the same opening, set
your compass at B and make an
identical arc, so that it intersects the
arc you made in step 2. Label this
point C.
Given a line l and a point P not on l, construct a line through P,
perpendicular to line l.
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Step 4: Draw PC
P
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PC ^ AB
B
A
l
C
: The proof of this fact involves the
use of congruent triangles.
Given a segment, construct its perpendicular bisector.
Step 1: Open your compass so that
when you place the point of the compass
at A the compass extends more than
halfway to B, and make an arc above
and below AB .
D
Put compass
point here
A
B
Put compass
point here
C
suur
suur suur
CD ^ AB and CD bisects AB
Step 2: Using the same opening, place
the point of your compass at point B
make a similar arc so that it intersects
the arc in step 1 twice. Label the two
intersection points C and D.
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Step 3: Draw CD
: The proof of this fact involves the
use of congruent triangles.