Name ________________________________
CONSTRUCTION #1: Segment Copy
Pd ___
Objective: Given a line segment, construct a line segment congruent to the given one.
Procedure:
1. Draw a working line on your paper.
2. Choose a point on the working line and label it.
3. Set the compass point/viewing hole over one endpoint of the given line segment, and place pencil
point/slide the radius indicator so that one of its holes is over the other endpoint. Draw a small arc
intersecting this endpoint.
4. Keeping the pencil point/radius indicator of the compass in the same place, put the compass point
over the labeled point on your working line.
5. Draw a small arc intersecting your working line and label the point of intersection.
Practice: Construct copies of each of these segments:
A
B
H
G
M
N
CONSTRUCTION #2: Angle Copy
Objective: Given an angle, construct an angle congruent to the given one.
Procedure:
1. Use the straightedge to draw a ray. Label its endpoint Q.
2. Place the compass point/viewing hole over the vertex of the given angle. Draw an arc that intersects
both sides of the angle. Label these two points of intersection R and S.
3. Keeping the radius of the compass the same, place the compass point/viewing hole over Q. Draw an
arc that intersects the ray. Label this point of intersection T.
4. Place the compass point/viewing hole over R. Slide the radius indicator until it is over S.
5. Using this new radius setting, put the compass point over T. Draw an arc that intersects the one you
drew in step 3. Label the point of intersection U.
6. Draw ray QU.
Practice: Construct copies of each of these angles:
CONSTRUCTION #3: Perpendicular Bisector
Objective: Given a line segment, construct the perpendicular bisector of the segment.
Procedure:
1. Place the compass point viewing hole over one endpoint of the given segment.
2. Set the pencil point/radius indicator so that it is slightly more than half the length of the given
segment, and draw arcs above and below the segment.
3. Keeping the radius of the compass the same, place the compass point on the other endpoint of the
given segment and draw arcs above and below the segment. These arcs should intersect the arcs you
drew in step 2.
4. Use the straightedge to draw a segment between the two points of intersection of the arcs. This
segment is the perpendicular bisector of the given segment.
Practice: Construct the perpendicular bisectors of these segments:
P
Q
R
Y
S
Z
CONSTRUCTION #4: Angle Bisector
Objective: Given an angle, construct the bisector of the given angle.
Procedure:
1. Place the compass point/viewing hole over the vertex of the given angle. Draw an arc that intersects
both sides of the angle. Label these two points of intersection A and B.
2. Place the compass point over B and slide the radius indicator out until the radius hole is in the
interior of the angle. Draw an arc in the interior of the angle.
3. Without changing the radius indicator, place the compass point over A and draw an arc that
intersects the one you drew in step 2. Label the intersection point C.
4. Draw a ray extending from the vertex of the angle through point C.
Practice: Construct the bisectors of each of these angles:
CONSTRUCTION #5: Perpendicular Through A Point Off The Line
Objective: Given a line and a point not on the line, construct the perpendicular to the line through the point.
Procedure:
1. Select a compass setting. Place the compass point/viewing hole on the given point and draw two
arcs that intersect the given line--one to the right and one to the left of the given point. Label these
points of intersection V and W.
2. Adjust the compass radius indicator so that it is a little longer than half the length of segment VW.
Place the compass point on V and draw an arc above the given line.
3. Without changing the setting, place the compass point on W and draw an arc above the given line
intersecting the arc you drew in step 2. Label the intersection of the arcs X.
4. Use the straightedge to draw a line through point X and the given point. This line will be
perpendicular to the given line.
Practice: Construct the perpendiculars to each of these lines through the given points:
Z●
n
m
Q●
●P
k
CONSTRUCTION #6: Perpendicular Through A Point On The Line
Objective: Given a line and a point on the line, construct the perpendicular to the line through the point.
Procedure:
1. Place the compass point/viewing hole over the given point and draw an arc that intersects the given
line on either side of the point. Label the points of intersection G and H.
2. Adjust the compass radius indicator so that it is a little longer than half the distance between the
given point and the arcs you drew. Place the compass point on G and draw an arc below the given
line.
3. Without changing the setting, place the compass point on H and draw an arc below the given line
intersecting the arc you drew in step 2. Label the intersection of the arcs K.
4. Use the straightedge to draw a line through point K and the given point. This line will be
perpendicular to the given line.
Practice: Construct the perpendiculars to each of these lines through the given points:
●
P
m
h
●S
g
● U