Download Basic Geometric Constructions When constructing

Basic Geometric Constructions
When constructing basic geometric figures, you cannot use a ruler to
find the lengths of the sides and estimate the angles. Basic geometric
constructions require the use of a geometric compass. One type of
compass has a point on one side and a pencil on the other side (see
figure below).
Figure of Geometric Compass
The following is a list of basic geometric constructions that we cover.
Please watch the video to see how these constructions are done.
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Congruent segments
Congruent angles
Perpendicular bisector
Angle bisector
Constructing Congruent Segments
Have the same length
Construction based on congruent radii of congruent circles
Constructed using following steps
• Put point of compass on one end and pencil tip on
the other end and draw an arc
• Draw a new point somewhere
• Place the point of compass on new point and draw
arc of equal length
• Draw segment from point to arc
Original Line Segment
Copied Line Segment
© LaurusSoft, Inc. 2010
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Constructing Congruent Angles
Have the same measure between sides
Constructed using following steps
• Copy one of the segments using process above
• Pick a point on the copied segment and draw an arc
through that point
• Using the intersection of the arc you just drew and
the chosen point, create a second arc that intersects
the first arc
• Copy the other segment that makes up the angle
Original Angle
Copied Angle
B’
B
5
5
C’
C
4
4
A
A’
Steps for Constructing Congruent Triangles
1. follow the steps above
2. Draw in third side
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Perpendicular Bisector of a Line Segment
Forms 90o angle
Cuts through midpoint of the segment
This construction can be used whenever you are needing to locate the
midpoint or needing to construct a line perpendicular to another line.
© LaurusSoft, Inc. 2010
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Steps for Constructing Perpendicular Bisector
Put point of compass at one of the endpoints
Expand compass more than half way and draw large
arc
Put point of compass at other endpoint
Keeping the compass at the same distance, draw
another large arc (the arcs should intersect each other
above and below the segment)
Draw a line segment through the two points of
intersection of the two arcs
Constructing Angle Bisector
Put point of compass at vertex and draw an arc that
cuts through both sides of angle
Put point of compass at one intersection point and
draw arc in middle of angle
Keeping the compass at the same distance, draw
another arc from the other point of intersection (the
arcs should intersect each other inside the angle)
Draw a line segment through the vertex and
intersection of the two arcs inside the angle
B
C
A
© LaurusSoft, Inc. 2010
Points of Concurrency
Points of concurrency are the points where certain line segments
constructed from the parts of a triangle intersect. You should be
able to locate all of these points through constructions.
Incenter – intersection of the three angle bisectors (construct
all three angle bisectors)
Circumcenter – intersection of the three perpendicular
bisectors (construct all three perpendicular bisectors)
Centroid – intersection of the three medians (construct all three
perpendicular bisectors to find the midpoints of each side and
connect each midpoint to opposite vertex)
Orthocenter – intersection of the three altitudes (see video for
this construction)
© LaurusSoft, Inc. 2010