7th Grade Pre-Algebra
OPTIONAL
CONSTRUCTION PROJECT
The project is worth 80 points and will be part of the fourth quarter grade if you choose
to complete it. The first five of the assignments must be completed. The sixth
assignment may be done for up to ten extra credit points. This project can greatly
improve your fourth quarter grade, so do not put it off to the last minute! If you score
less than your 4th quarter test average on this project, it will not be counted so as to not
decrease your grade. (It can only help it.)
Each assignment will be worth 16 points. 12 points will be given for overall
observations, accuracy and generalizations. 4 points for neatness (can I see and follow
all construction marks and understand what you did and how you did it.) In order to
receive full credit, all construction marks must be clearly visible.
REMEMBER: Facts cannot be determined from the constructions. Please use phrases
such as “It appears as if…” and “It would seem as if…”
Ask me questions and do not put this project off. It is time consuming, but an easy way
to boost your test/project category. I will not give help on projects after Friday, May 6 th.
The project must be turned in by 3:30 PM on May 16th. Absolutely no exceptions.
Also, a great reference to use when completing these projects can be found at
www.mathopenref.com. If you look at the index under constructions, there are many
hints, tips, and tricks on how complete different components. You will need to use this
site to complete this project.
Each part of each assignment should be drawn on a separate sheet of paper. All
constructions should be drawn on white computer paper. Generalizations should be
typed or neatly handwritten.
ASSIGNMENT 1
1. Draw a triangle and construct the perpendicular bisectors of its sides. Repeat for
three other triangles of differing shapes (therefore having a total of 4). Record an
observation for each triangle. State a generalization based on what you observed.
2. Draw a triangle and construct all of the altitudes. Repeat for three other triangles of
differing shapes. (Be sure you have one obtuse triangle.) Record an observation for
each construction. State a generalization based on what you observed.
3. Draw a triangle and construct the medians for each side. Repeat for three other
triangles of differing shapes. Record an observation for each triangle. State a
generalization based on what you observed.
ASSIGNMENT 2
1. Draw an acute triangle and construct the orthocenter, the centroid and the
circumcenter. (You can find these definitions below.) State your observation
on the relationship of these three points. Repeat the process for an obtuse triangle
and a right triangle. State a generalization based on what you observed.
2. Draw a triangle RST. Construct the medians. Name the centroid C. Measure the
medians in centimeters and record the measurement in your observations. Measure
RC, SC, and TC in centimeters and record the measurements in your observations.
What is the relationship of these measures to each other? Repeat this experiment
on two other triangles of differing shapes. State a generalization based on what
you observed.
ASSIGNMENT 3
1. Construct isosceles triangle RST so that RS and RT are congruent. Bisect angles S
and T. Draw the line determined by the intersection of the bisectors and R. Record
how this line is related to ST in your observations. Repeat for two other isosceles
triangles. State a generalization based on what you observed.
2. Draw a triangle and construct the bisector of one side. Name that midpoint P.
Construct a line parallel to one side of the triangle and through point P. Record in
your observations where this line intersects the third side of the triangle. (Make sure
you support your observations.) Repeat for two other triangles of different shapes.
State a generalization based on what you observed.
3. Draw a scalene triangle RST. Label the side opposite angle R as r. Do likewise for
sides s and t. Measure all three sides in centimeters and all three angles and record
your measurements in your observations, arranged from largest to smallest. Repeat
this experiment for two other scalene triangles of different shapes. State a
generalization based on your observations.
ASSIGNMENT 4
1. Draw an odd shaped quadrilateral that does not cross itself. Construct the bisector
of each side. Label these midpoints A, B, C, D. Connect these points to form
quadrilateral ABCD. What do you notice about this quadrilateral? Record your
observations and the support for your observations. Repeat for two other
quadrilaterals of differing shapes. State a generalization based on your
observations.
2. Construct parallelogram ABCD and draw its diagonals. Label the point where the
diagonals intersect as P. Measure in centimeters and record in your observations
the lengths of AP and CP. Compare their lengths. Record and compare the lengths
of BP and DP. Repeat the experiment for two other parallelograms of differing
shapes. State a generalization based on your observations.
3. Construct a rhombus. Draw its diagonals. Measure and compare the four angles
created at the intersection of the diagonals in your observations. Repeat the
experiment two more times with rhombi of differing shapes. State a generalization
based on your observations.
ASSIGNMENT 5
1. Construct a rectangle and the bisector of each side. Connect the midpoints of the
sides to form a quadrilateral. Record the type of quadrilateral that is formed along
with your proof in your observations. Repeat the experiment for two more
rectangles. State a generalization based on your observations.
2. Construct parallelogram ABCD. Draw in its diagonals and label their point of
intersection O. Bisect AO, BO, CO, and DO and call the midpoints E, F, G, and H.
Draw quadrilateral EFGH. In your observations, describe what type of quadrilateral
EFGH is, along with your proof. How does EFGH relate to ABCD? Repeat the
experiment one more time. State a generalization based on your observations.
3. Construct a circle and mark two points A and B so they are NOT opposite ends of a
diameter. The two points then determine a major arc and a minor arc. Choose point
T on minor arc AB. Draw AT and BT. Measure angle ATB. Repeat for two other
points on minor arc AB. Record your findings in your observations. Choose point K
on major arc AKB. Draw AK and BK. Measure angle AKB. Repeat for two other
points on major arc AKB. Record your findings in your observations. State a
generalization based on your observations.
ASSIGNMENT 6
1. Construct a large circle with point O at its center. Choose points A, B, and C on
the circle so that neither AB or BC is a diameter. Construct the perpendicular
bisector for AB and BC. Repeat this process with points E, F, and G on the same
circle. Now on a clean sheet of paper, choose any three noncollinear points R, S,
and T. Construct THE circle hat contains these three points. Explain what you
observed and how you used that observation in the second part of this experiment.
2. Draw segment AB and construct the perpendicular bisector of AB. Choose point T
to be any point on the bisector. Draw AT and BT. Measure them in centimeters and
record the measurement in your observations. Record how the lengths compare.
Repeat the process for three other points on the bisector. Choose point K to any
point NOT on the bisector. Draw AK and BK. Measure them in centimeters and
record the measurement in your observations. Record how the lengths compare.
State a generalization based on your observations.
3. Construct a large circle and any chord AB on it. Bisect the chord and label the
midpoint M. Draw two additional chords each containing the point M. Connect the
endpoints of the two new chords so that the connecting segments cross AB. Label the
points where these connecting segments intersect AB and S and T. Measure lengths
MS and MT in centimeters and record them in your observations. Repeat the
experiment two more times with different circles drawing chords in different positions.
State a generalization based on your observations.
Definitions
Altitude – the line segment that travels from the vertex of a triangle to the other
side and meets the opposite side at a right angle.
Orthocenter – the point where three altitudes of a triangle meet.
Median – the line segment that travels from the vertex of a triangle to the
midpoint of the opposite side.
Centroid – the point where the three medians of a triangle meet.
Circumcenter – the point where the three perpendicular bisectors of a triangle
meet.
Major arc – a part of a circle that comprises more than half of the circle.
Minor arc – a part of a circle that comprises less than half of the circle.
Collinear – on the same line