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Page 1: Cover page with your name, my name, date, block, and Islamic art design you created using
compass and straight edge. Color your design.
publications/pdfs/islamic_geometric/islamic_art_and_geometric_design.pdf
Page 2: Acute, scalene triangle with Euler line constructed. See instructions in this packet.
Page 3: Obtuse, scalene triangle with 9-point circle constructed. See instructions in this packet.
Page 4: 2nd tic-tac-toe choice.
Page 5: 3rd tic-tac-toe choice
Page 6: Writing Component (one page using three sources). Choose one of the following topics:
o A description of the geometry of Islamic art.
o Short biography of Euler and his discovery of the Euler line.
o History of tangrams and their present use today.
o Summary of findings about Napolean’s theorem. Did he discover it; if not him, who? Was
he friends with any other important mathematicians? Who? Research von Aubel’s theorem.
How is it related to Napolean’s theorem?
o Summary of the three famous impossible geometric constructions.
Page 7: Bibliography using MLA format. You must list at least three sources. Only two can be
electronic resources
IMPORTANT!
 You must complete three activities in a row (horizontally, vertically or diagonally)!
 You must include a one-page writing component which does not need to relate to your three
constructions.
 You must complete each construction on a separate sheet of paper labeled with the title of the
activity. Show all construction markings.
 Follow directions carefully for your chosen activities.
 The writing component and bibliography must be typed.
Square design
Dodecagon
Tangram
Islamic Art
(design or your
Euler Line
choice)
Nine Point Circle
Kite
Napoleon’s
Triangle Theorem
Tangram
(candle/swan)
Pentagon
Inscribe VS.
Circumscribe
Euler Line
1.
2.
3.
4.
5.
6.
Use a straightedge to draw an acute scalene triangle; no side should be less than 8cm long.
Construct the orthocenter. Label it W using a blue writing utensil.
Construct the centroid. Label it X using a red writing utensil.
Construct the circumcenter. Label it Y using a green writing utensil.
Construct the incenter. Label it Z in pencil.
Show which three of these four points are collinear by drawing the line they contain.
Label it Euler line!
Nine Point Circle
1. Use a straightedge to draw an obtuse scalene triangle.
2. Construct the perpendicular bisectors of each side to find the midpoints. These three midpoints are
the first three points of the circle. Label the points A, B, and C.
3. Construct a perpendicular segment from each vertex to the opposite side. The intersection of the
sides and the perpendicular segments are the next three points of the circle. The points are called the
altitude bases. Label the points D, E, and F.
4. Construct the orthocenter. Label it G.
5. Construct the midpoints of the segments from the orthocenter to each vertex. These midpoints are
the last three points of the circle. Label them H, J, K. (Yes, “I” was intentionally skipped.)
6. Connect the midpoints of original the triangle.
7. Find the circumcenter of the triangle made by the midpoints. Label it Z. This is the center of the
nine point circle.
8. Draw a circle with center Z and radius out to any of the nine points.
Islamic Art Design
Create an Islamic art design by repeating a small number of geometric elements such as a circle, a
square, or straight lines. Combine, duplicate, and interlace the elements to create an intricate pattern as
shown. Color your design. Resources: Mrs. Wenzel or http://www.metmuseum.org/explore/
publications/pdfs/islamic_geometric/islamic_art_and_geometric_design.pdf.
Square design
1. Construct a square with a diagonal length of 8 cm inside a circle
2. Construct the angle bisectors for the angles made by the diagonals and the sides of the square.
3. Find the “star like” region AND color in the “star-like region.
A
A
B
Dodecagon
1. Construct a circle with any given radius  2 inches.
2. Inscribe a regular dodecagon in this circle.
3. Include a brief description of your procedure.
B
Construct a Tangram
The pieces of a tangram can be used to create many interesting figures. They can also be used to analyze
relationships among each other. Follow the given set of instructions to make your own tangram pieces.
1. On a piece of graph paper, label the x-axis from –16 to 16 and the y-axis from –16 to 16.
2. Plot and label the following points: A(–16, 16), B(16, 16), C(16, –16), and D(–16, –16).
3. Use a ruler to construct segments AB, BC, CD, and DA.
4. Draw segment BD.
5. Find the midpoint of AB. Label it E.
6. What are the coordinates of point E?
7. Find the midpoint of AD. Label it F.
8. What are the coordinates of point F?
9. Draw EF.
10. Find the midpoint of EF. Label it G.
11. What are the coordinates of point G?
12. Draw CG.
13. Find the intersection of GC and BD. Label it H.
14. What are the coordinates of point H?
15. Find the midpoint of HD and label it J.
16. What are the coordinates of point J?
17. Draw GJ.
18. Find the midpoint of HB and label it K.
19. What are the coordinates of point K?
20. Draw EK. You should now have seven pieces constructed.
21. Now use all 7 pieces to make the swan, candle, or a puzzle
of your choice.
22. Glue the 7 pieces on a piece of paper.
23. Write the coordinates for E, F, G, H, J, and K underneath.
The Construction of the Pentagon
1. Construct a circle with center O.
2. Pick a point anywhere on the circle, say X, and with the straightedge, draw a line through O, until it
intersects the circle again at X'. The radius of the circle is OX = OX'.
3. Bisect the segment XX' with the compass. Label the points where the bisector intersects the circle A
and Q.
4. Find the midpoint of OX'. Label it P.
5. Use the straightedge to draw AP.
6. Use the compass to mark the distance AP and transfer it to XX'. Do this by pinning the compass at P,
with length AP, and drawing an arc down to XX'. Mark that point as G. Now AP = PG and the
distance AG is the side of the pentagon. (AG > AP).
7. Use the compass to mark the distance AG, Starting with A, walk the compass around the circle
creating points C, D, and E.
8. Use the straightedge to connect the vertices of the pentagon.
Kite
1.
2.
3.
4.
5.
6.
7.
Research the definition of the quadrilateral called kite.
Construct a kite.
Draw the diagonals. What is special about the diagonals?
Construct another kite.
Construct the midpoints of all sides, then connect the midpoints.
What quadrilateral is formed?
Write the definition and the answers to the above questions below your constructions.
Napoleon’s Triangle Theorem
Napoleon’s theorem states: When equilateral triangles are constructed on each side of any triangle, the
centers of these equilateral triangles will form a new equilateral triangle.
1.
2.
3.
4.
Use a straightedge to draw a scalene triangle.
On each side if this triangle, construct equilateral triangles.
Construct the center of each of these three equilateral triangles.
Connect these center points and according to Napoleon you should have an equilateral triangle.
Inscribe vs. Circumscribe
1.
2.
3.
4.
5.
Construct an isosceles triangle where the legs are double the base length.
Inscribe a circle in that isosceles triangle.
Use a straightedge to draw a scalene triangle.
Circumscribe a circle about the scalene triangle.
Underneath the constructions, briefly explain how these two constructions (inscribe vs.
circumscribe) are different.