Constructing an Image line segment congruent to an original given line segment.
1. To construct a line segment congruent to an original line segment,
2. Place the compass bull's-eye on endpoint A and adjust the
begin by drawing an original segment AB and an image ray with
radius so it will draw an arc thru the other endpoint B. Without
endpoint C.
changing the compass radius, place the bull's-eye on point C
and draw an arc crossing the ray. Label the intersection point
as point D, mark the tic marks to indicate congruent parts and
then Box a congruence statement as shown.
Original
A
B
Original
Image
Image
A
C
B
C
AB  DC
D
Bisecting line segment.
1. To bisect a line segment, begin by drawing an original segment AB.
2. Place the compass bull's-eye on endpoint A and adjust the
Note: you do not have an "Image" side to this construction.
radius so it is more than half the distance AB and then draw a
full semicircle arc thru the segment.
A
A
B
B
3. Without changing the compass radius, place the bull's-eye on the
4. Use the straightedge to draw line as shown the splits the
other endpoint B and draw a similar semicircle. This creates the
"fish-eye". Mark the point P where it intersects AB, make the
figure we refer to as the "Fish-Eye"
tic marks to indicate congruent parts and then Box your
congruence statement as shown.
A
A
P
B
B
AP  PB
Adding line segments onto an Image ray.
1. Begin by drawing two original non-congruent line segment AB and
2. Copy segment AB onto the image ray as show previously
CD and an image ray with endpoint E.
starting with endpoint E. Label the new endpoint F and make
the tic marks to indicate congruent parts.
Original
A
Original
Image
C
A
E
B
C
E
B
D
Image
F
D
3. Place the bull's-eye on endpoint C and adjust the radius for distance CD, drawing an arc thru D. Without changing the compass
radius, place the bull's-eye on the image point F and draw an arc crossing the ray. Label the new intersection point as point G, mark the
double tic marks to indicate congruent parts and then Box a statement as showing the resultant construction. (note there are no "bars"
above the segments because the statement indicates the measures are added, not the actual segments)
Original
Image
A
C
AB + DC = EG
E
B
D
F
G
Constructing an Image angle congruent to an original given angle.
1. To construct an angle congruent to an original angle, begin by
2. Place the compass bull's-eye on point A and draw a
drawing an original angle A and an image ray endpoint D.
measuring arc across both sides of the angle. Without
changing the compass radius, place the bull's-eye on point D
and draw a similar arc crossing the ray. Label the three
intersection points as shown.
Original
Image
Original
Image
D
A
3. Span the compass so that its radius is BC. Place the compass
4. Use the straightedge to draw ray DF. Make the tic marks to
bull's-eye on point E and draw an arc intersecting the one drawn in
indicate congruent parts and then Box your congruence
the previous step. Label the intersection point F.
statement as shown.
Original
Image
Original
BAC  EDF
Image
Construct the bisector of an angle.
1. Let point P be the vertex of the
angle. Place the compass on point
P and draw an arc across both
sides of the angle. Label the
intersection points Q and R.
2. Place the compass on point Q
and draw an arc across the interior
of the angle.
3. Without changing the radius of
the compass, place it on point R
and draw an arc intersecting the
one drawn in the previous step.
Label the intersection point W.
4. Using the straightedge, draw ray
PW. This is the bisector of QPR...
Make tic marks indicating the
congruent angles and Box your
congruence statement
QPW  WPR
Adding angles onto an Image ray.
1. Begin by drawing two original non-congruent angles A and
3. Copy B onto the new image ray EG. Try to make the new
B and an image ray with endpoint E.
measuring arc larger than previously, and make sure the image side
Original
starts on the new ray EG and continues in the same direction as in
Image
step 2 (CW). Label the new ray EH, mark the double tic marks to
indicate congruent parts and then Box a statement showing the
resultant construction. (note you need to add the "m" before the 
symbol to indicate the measures are added, not the actual angles)
A
Original
E
B
Image
3B
mA + mB =- m FEH
F 
2. Copy A onto the image ray as show previously using
G
measuring arcs 1A and 1B, and spanning arcs 2B and 2B.
Label the two rays EF and EG and make the tic marks to
A
indicate congruent parts.
1A
Original
E
3A
Image
4B
1B
F 


G
E
A
2A
B

H
B
2B
4A
Subtracting line segments onto an Image ray.
1. Begin by drawing two original non-congruent line segment AB and
2. Copy the longer segment CD onto the image ray starting
CD and an image ray with endpoint E.
with endpoint E. Label the new endpoint F and DO NOT make
the tic marks to indicate congruent parts.
Original
A
Original
Image
C
A
E
B
C
E
B
D
Image
F
D
3. Span the distance AB, drawing an arc thru B. Without changing the compass radius, place the bull's-eye on the image point F and
swing the radius 180 degrees back towards the endpoint E. Now draw an arc crossing the ray (note the arc should open in the
opposite direction as before). Label the new intersection point as point G, make a tic marks to indicate congruent parts and then Box a
statement as showing the resultant construction.
Original
Image
C
A
DC - AB = EG
E
B
D
G
F