Basic Constructions
I. Copy a segment
II. Copy an angle
What is a Construction?
• Uses TWO instruments only
– Compass
– Straightedge
• Since a compass measures the radius of a circle,
and radii of a circle are congruent, then we can use
it to construct congruent segments.
• A straightedge is used to connect two points. A
ruler may not be used to measure distances in
constructions.
What is a Construction?
• Definition:
– An arc is any part of a circle.
–When we draw using a compass we will be
drawing arcs. We rarely need to complete the
entire circle. The radii will still be congruent even
if a complete circle is not present.
Construction #1: Copy a Segment
Given AB , construct a segment congruent to AB on line l.
A
Step 1: Use the straightedge to
draw a line and label it l
B
Step 2: Choose any point on l
and label it C.
Put compass
point here
Step 3: Set the compass at A
and make an arc at B.
AB  CD
l
C
D
Put compass
point here
Step 4: Using the same
opening, set your compass at C
and make an identical arc so
that it intersects line l. Label
this point D.
Construction #2: Copy an Angle
Step 1: You need to start with a
line l and a point F which
corresponds to C.
E
Step 2: Opening your compass
to any comfortable distance, set
the compass at C and make an
arc that intersects both sides of
the angle. Label these points E
and D.
Step 3: Using the same opening,
set the compass at F and make
an identical arc which intersects
the line l. Label this point G.
Put compass
point here
C
D
Put compass
point here
Put compass
point here
l
F
G
Step 4: On the original angle,
set the compass at D and make
an arc that intersects the other
side of the angle at E.
Construction #2: Copy an Angle
Step 5: Using the same opening,
set your compass at G and make
an identical arc so that it
intersects the arc from step 3.
Label this point H.
E
Step 6: Draw FH
C
D
ECD 
H
Put compass
point here
F
G
HFG