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Name_____________________________
Period________Date_________________
CONSTRUCTION PROJECT
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You can use only a pencil, straightedge and compass.
The only measuring tool that you can use is the compass. NO PROTRACTORS.
NO RULERS (other than to use as a straightedge)
Leave all of your construction arcs, segments and lines that you draw to complete
each exercise.
If you need to erase an error, please be thorough and erase all of the error.
Precision and accuracy are very important! Sharpen your pencil and compass pencil
often.
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You may NOT do this project on a computer.
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This project counts as a TEST GRADE!!
Deadline: Monday, Sept. 19th (A)
or Tuesday, Sept. 22nd (B) at the
beginning of class
****10 points off for each late day
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CONSTRUCTION PROJECT
1. Construct a copy of segment AB
1.
Begin by drawing a ray with endpoint A’.
2. Place the compass at point A. Adjust the compass radius so that it is the same length as segment AB.
3. Without changing the compass radius, place the compass on the endpoint A’. Draw an arc intersecting
the ray. Label the intersection point B’.
4. AB = A’B’
A
B
2. Construct an angle congruent to a given angle.
1.
To draw an angle congruent to  A, begin by drawing a ray with endpoint D.
2. Place the compass on point A and draw an arc across both sides of the angle. Label the two
intersection points on  A B and C. Without changing the compass radius, place the compass on point
D and draw a long arc crossing the ray. Label the intersection point on the ray E.
3. Set the compass so that its radius is BC. Place the compass on point E and draw an arc intersecting on
the one drawn in the previous step. Label the intersection point F.
4. Use the straightedge to draw ray DF.
5.
 EDF   BAC
A
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3. Construct the perpendicular bisector of a line segment. This is also how you can…a) construct the
midpoint of a line segment, and… b) construct a 90oangle.
1.
Begin with given line segment XY.
2. Place the compass at point X. Adjust the compass radius so that it is more than (½)XY. Draw two
large arcs above and below the line segment.
3. Without changing the compass radius, place the compass on point Y. Draw two arcs intersecting the
previously drawn arcs. Label the intersection points of the two pairs of arcs with A and B.
4. Using the straightedge, draw line AB. Label the intersection point M. Point M is the midpoint of line
segment XY, and line AB is perpendicular to line segment XY.
Y
X
4. Given a line and a point on the line, construct a line through the point, perpendicular to the given line.
1.
Begin with given line k, containing point P.
2. Place the compass on point P. Using an arbitrary radius, draw arcs intersecting line k , one to the left
of P and one to the right. Label the intersection points X and Y.
3. Place the compass at point X. Adjust the compass radius so that it is more than (½)XY. Draw an arc
above the point P.
4. Without changing the compass radius, place the compass on point Y. Draw an arc intersecting the
previously drawn arc. Label the intersection point A.
5. Use the straightedge to draw line AP. Line AP is perpendicular to line k.
P
k
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5. Given a line and a point not on the line, construct a line through the point, perpendicular to the given line.
1.
Begin with given line k and given point R not on the line.
2. Place the compass on point R. Using an arbitrary radius, draw arcs intersecting line k at two points.
Label the intersection points X and Y.
3. Place the compass at point X. Adjust the compass radius so that it is more than (½)XY. Draw an arc
below line k and beneath point R.
4. Without changing the compass radius, place the compass on point Y. Draw an arc intersecting the
previously drawn arc. Label the intersection point B.
5. Use the straightedge to draw line RB. Line RB is perpendicular to line k.
R
k
6. 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 a long 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.
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7. Given a line segment as one side, construct an equilateral triangle.
This method may also be used to construct a 60º angle.
1.
Begin with given line segment TU. Place the compass at point T, and set the compass radius to have
the same length as TU. Now draw a long arc above the midpoint of segment TU.
2. Keeping the same radius, place the compass at point U and draw another arc intersecting the first one.
Let point V be the point of intersection.
3. Draw line segments TV and UV. Triangle TUV is an equilateral triangle, and each of its interior angles
has a measure of 60º.
U
T
8. Construct the center point of a given circle.
1.
Begin with the given circle. Draw chord AB. A chord is a segment whose endpoints lie on the circle.
2. Construct the perpendicular bisector of chord AB. Let C and D be the points where it intersects the
circle. (Refer to the construction of a perpendicular bisector on page 2.)
3. Chord CD is a diameter of the circle. Construct point P, the midpoint of diameter CD. Point P is the
center point of the circle. (Refer to the construction of the midpoint of a line segment, on page 2.)
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9. Given segments a, b and c, construct a segment with length (2a + b).
c
b
a
Do not do your
construction within
this box.
10. Given segments b and c (above,) construct a segment with length (2c - b). Label the endpoints of your
answer segment with x and y.
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11. Construct a triangle with sides congruent
to the given segments a, b and c. You may
not use a ruler to measure any lengths. No
arcs, not credit!
c
b
a
Do not do your
construction
within this box
12. Construct a square with sides the length of the given segment. You may not use a protractor or any
other measuring device other than a compass. Construct the 90 oangles with a compass! Refer to problem
#3.
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13. Construct an angle with a measure of 30º. Hint: You know how to construct a 60o angle without a
protractor! Write in 30oon your answer angle.
14. Follow the instructions to construct an isosceles triangle with equal sides having the length of the given
segment and a vertex angle of 45o.
a. Below construct a 45oangle. (hint: construct a 90oangle)
b. Using your 45oangle, construct an isosceles triangle with
equal sides having the length of the given segment.
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15. Follow the instructions to construct a triangle that has two sides congruent to the given line segments,
and has an angle created by the intersection of these two segments that is equal in measure to given K .
K. Label the
a)
Construct an angle congruent to
vertex K’.
b)
Using angle K’, construct a triangle with two sides
congruent to the given segments a and b that
intersect to form angle K’.
Do not do your
constuction inside
this box.
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