DIRECTIONS FOR GEOMETRY HONORS CONSTRUCTION PROJECT

Transcription

1 Name Period DIRECTIONS FOR GEOMETRY HONORS CONSTRUCTION PROJECT Materials needed: Objective: Standards: 8 pieces of unlined white computer / copy paper (8.5 in. by 11in.), compass, ruler, protractor, pencil, and markers/colored pencils. Use geometric construction techniques to create a how-to book detailing the step-by-step instructions for tripling a segment, doubling an angle, bisecting an angle, an equilateral triangle, a regular hexagon, a square, and 1 design. MAFS.912.G-CO.3.11: Make formal geometric constructions with a variety of tools and methods. Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. MAFS.912.G-CO.4.13: Construct an equilateral triangle, a square, and regular hexagon inscribed in a circle. Grading: Extra Credit: Due Date: See Rubric below for point distribution. Late projects will receive a 10 point deduction per week it is late with the 1 st week beginning the day after the due date. Students can receive up to 10 points extra credit for turning their project into a how to book. Requirements for the extra credit include (1) designing a cover page with a title and illustration, (2) writing/typing each step in words and placing them underneath the step in the construction, and (3) pages must be bound. Title page may be typed and printed or hand drawn. Binding can be yarn, project covers, or scrapbook. Be creative! Wednesday September 19 th. No projects will be accepted after Wednesday October 10 th. Page Order for the How to Book 1. Tripling a Segment 2. Doubling an Angle 3. Bisecting an Angle 4. Regular Hexagon 5. Equilateral Triangle 6. Square 7. Blueprint Design 8. Professional Design

2 Name Period Grading Rubric: Points earned/points possible Construction Comments / 10 points Tripling a Segment / 10 points Doubling an Angle / 10 points Bisecting an Angle / 15 points Regular Hexagon / 15 points Equilateral Triangle / 15 points Square / 20 points Design / 5 points Page Headings and Step Labels / 10 points Extra credit / -30 points Late penalty (10pts per week late) /100 points Total Score How to Example: Every step gets a diagram!

3 Tripling a Segment Step #1: (2 pts) Use a ruler to draw AB with a length of 5 cm. Step #2: (2 pts) Construct LI such that LI = AB. Step #3: (2 pts) Construct IN such that IN = AB and points L, I, and N are collinear. Step #4: (4 pts) Construct NE such that NE = AB and points L, I, N, and E are collinear. Congratulations! LE = 3AB. Doubling an Angle Step #1: (2 pts) Using a protractor, draw XYZ such that mxyz = 70. Step #2: (4 pts) Construct BAT such that mbat = mxyz. Step #3: (4 pts) Construct CAB such that mcab = mxyz. CAB and BAT are adjacent angles. Congratulations! mcat = 2 mbat. Constructing an Angle Bisector Step #1: (2 pts) Using a protractor, draw PUN such that mpun = 120. Step #2: (8 pts) Construct the bisector of PUN. Label the bisector UF. Congratulations! You have now put some FUN in this PUN! Regular Hexagon Step #1: (3 pts) Construct F with a radius of 4 cm. Step #2: (6 pts) Using the same compass setting, construct 6 equally spaced arcs on the circle. Label the intersections of the arcs and F points E, U, C, L, I, and D consecutively. Step #3: (6 pts) Using a straightedge, draw EU, UC, CL, LI, ID, and. DE Congratulations! You have just constructed a regular hexagon inscribed within a circle!

4 Equilateral Triangle Step #1: (3 pts) Construct A with a radius of 4 cm. Step #2: (6 pts) Using the same compass setting, construct 6 equally spaced arcs on the circle. Label the intersections of the arcs and A points B, C, D, E, F, and G consecutively. Step #5: (6 pts) Using a straightedge, draw BD, DF, and BF. Congratulations! You have just constructed an equilateral triangle inscribed within a circle! Square Step #1: (2 pts) Construct M with a radius of 4 cm. Step #2: (3 pts) Use a straightedge to draw and label diameter CB. Step #3: (5 pts) Construct the perpendicular bisector of CB. Label the intersections of M and the perpendicular bisector U and E. UE should be another diameter of M. Step #4: (5 pts) Using a straightedge, draw CU, UB, BE, and CE. Congratulations! You have just constructed a square inscribed within a circle!

5 Design: Interlocking Triangle Directions Follow instructions to create the selected design. Do not erase any labels or markings. This will serve as your blueprint. On a new piece of paper, create a 2 nd version of your design. This will be your professionally colored version. Before coloring, erase point names and any markings not needed to see the final design. 1. (1 pt) Construct P with a radius of 8cm. 2. (1 pt) Using the same compass setting, construct 6 equally spaced arcs on the circle. Label the intersections of the arcs and P points A, B, C, D, E, and F consecutively. 3. (2 pts) Draw AC, CE, and EA using a straightedge. 4. (2 pts) Draw BD, DF, and FB using a straightedge. You should have 2 interlocking triangles at this point. 5. (2 pts) Draw the diameters AD, BE, and CF using a straightedge. Name the points where the diameters intersect the sides of the triangles points G, H, I, J, K, L; respectively. 6. (2 pts) Draw GI, IK, KG, HJ, JL, and LH using a straightedge. These form the inner borders of your interlocking triangles. THIS ENDS YOUR BLUEPRINT. 7. (5 pts) ON A NEW PIECE OF PAPER repeat steps #1 6. Erase the point names A through L. Pick one of the interlocking triangles to shade in first. Shade in one side of the triangle, all except the upper quadrilateral. Rotate your design to the next side and shade the side in the same way as the first side, making sure to leave the upper quadrilateral unshaded. Rotate your design and repeat this process for the remaining side. 8. (5 pts) Color the second interlocking triangle with a different color. Erase any unused lines that are still showing. Do not erase the circle. Congratulations! You have just constructed interlocking triangles!

6 Design: Flower from a Hexagon Follow instructions to create the selected design. Do not erase any labels or markings. This will serve as your blueprint. On a new piece of paper, create a 2 nd version of your design. This will be your professionally colored version. Before coloring, erase point names and any markings not needed to see the final design. 1. (2 pts) Construct P with a radius of 8cm. 2. (2 pts) Using the same compass setting, construct 6 equally spaced arcs on the circle. Label the intersections of the arcs and P points A, B, C, D, E, and F consecutively. 3. (6 pts) With the same compass setting you used to construct the circle, draw arcs BF, AC, BD, CE, DF, and EA. Each arc should pass through point P. This will complete the six petals of the flower. THIS ENDS YOUR BLUEPRINT. 4. (5 pts) ONE A NEW PIECE OF PAPER repeat steps #1 3. Erase the point names A through F and P. Do not erase the circle. 5. (5 pts) Color your design. Congratulations! You have just constructed a flower!

7 Design: Six-Pointed Star Follow instructions to create the selected design. Do not erase any labels or markings. This will serve as your blueprint. On a new piece of paper, create a 2 nd version of your design. This will be your professionally colored version. Before coloring, erase point names and any markings not needed to see the final design. 1. (1 pt) Construct P with a radius of 8cm. 2. (1 pt) Using the same compass setting, construct 6 equally spaced arcs on the circle. Label the intersections of the arcs and P points A, B, C, D, E, and F consecutively. 3. (2 pts) Draw AC, CE, and EA using a straightedge. 4. (2 pts) Draw BD, DF, and FB using a straightedge. You should have 2 interlocking triangles at this point. 5. (2 pts) You should notice a small hexagon inside the interlocking triangles. Label the hexagon s vertices G, H, I, J, K, and L consecutively. 6. (2 pts) Use a straightedge to draw GJ, HK, and IL. 7. (2 pts) Draw the diameters BE, CF, and AD using a straightedge. THIS ENDS YOUR BLUEPRINT. 8. (4 pts) ON A NEW PIECE OF PAPER repeat steps #1 7. Erase the sides of the inner hexagon, and erase the point names A through L. You should now have 12 congruent, isosceles triangles. 9. (4 pts) Shade in every other triangle with a dark color (six in total). Shade in the remaining triangles with one or more light colors. Alternating dark colors with light colors will give the star a 3D effect! Congratulations! You have just constructed a six-pointed star!

8 Design: Interlocking Square Directions Follow instructions to create the selected design. Do not erase any labels or markings. This will serve as your blueprint. On a new piece of paper, create a 2 nd version of your design. This will be your professionally colored version. Before coloring, erase point names and any markings not needed to see the final design. 1. (1 pt) Construct C with a radius of 8 cm. Use a straightedge to draw and label diameter AB. 2. (2 pts) Construct the perpendicular bisector of AB. The two places where the perpendicular bisector intersects circle C, label them with a point. Name the points D and E. 3. (1 pt) Using a straightedge, draw AD, DB, BE, and. EA 4. (2 pts) Construct the angle bisector of ACE. With a straightedge, extend the angle bisector until it forms a 3 rd diameter for circle C. Name the endpoints of this diameter F and G. 5. (2 pts) Construct the angle bisector of ACD. With a straightedge, extend the angle bisector until it forms a 4 th diameter for circle C. Name the endpoints of this diameter H and I. 6. (1 pt) Using a straightedge, draw HF, FI, IG, and GH. You should now have 2 interlocking squares. 7. (1 pt) The diameters of the circle intersect with the sides of your squares at 8 points. Label these points J, K, L, M, N, O, P, and Q, consecutively. 8. (2 pts) Using a straightedge, draw JL, LN, NP, and PJ to create the inner border of one square. Using a straightedge, draw KM, MO, OQ, and QK to create the inner border of the second square. THIS ENDS YOUR BLUEPRINT 9. (4 pts) ON A NEW PIECE OF PAPER repeat steps #1 8. Erase the point names. Pick one of the interlocking squares to shade in first. Shade in one side of the square, all except the upper quadrilateral. Rotate your design to the next side and shade the side in the same way as the first side, making sure to leave the upper quadrilateral unshaded. Rotate your design and repeat this process for the remaining 2 sides. 10. (4 pts) Erase any unused segments inside the interlocking squares. Color the second interlocking square with a different color. It is your choice whether or not to erase the circle. Congratulations! You have just constructed interlocking squares!

9 Design: Pinwheel from a Square Directions Follow instructions to create the selected design. Do not erase any labels or markings. This will serve as your blueprint. On a new piece of paper, create a 2 nd version of your design. This will be your professionally colored version. Before coloring, erase point names and any markings not needed to see the final design. 1. (1 pt) Construct C with a radius of 8 cm. Use a straightedge to draw and label diameter AB. 2. (2 pts) Construct the perpendicular bisector of AB. The two places where the perpendicular bisector intersects circle C, label them with a point. Name the points D and E. 3. (1 pt) Using a straightedge, draw AD, DB, BE, and. EA 4. (2 pts) Construct the angle bisector of ACE. With a straightedge, extend the angle bisector until it forms a 3 rd diameter for circle C. Name the endpoints of this diameter F and G. 5. (2 pts) Construct the angle bisector of ACD. With a straightedge, extend the angle bisector until it forms a 4 th diameter for circle C. Name the endpoints of this diameter H and I. 6. (1 pt) Using a straightedge, draw HF, FI, IG, and GH. You should now have 2 interlocking squares. 7. (2 pts) The diameters of the circle intersect with the sides of your squares at 8 points. Label these points J, K, L, M, N, O, P, and Q, consecutively. Using a straightedge, draw JL, LN, NP, and PJ to create the inner border of one square. Using a straightedge, draw KM, MO, OQ, and QK to create the inner border of the second square. 8. (1 pt) Notice that the design intersects the circle 8 times with pairs of small, right triangles at each intersection. Erase the hypotenuse of the left triangle of each pair. THIS ENDS YOUR BLUEPRINT. 9. (4 pts) ON A NEW PIECE OF PAPER repeat steps #1 8. Observe that 8 parallelograms have been formed, with the 4 vertices as followed: one point on the circle, 2 points formed by the intersections of a diameter and the side of an outer square, and the 4 th point being unnamed. Shade in every other parallelogram with one color (4 total). 10. (4 pts) Shade in the remaining 4 parallelograms with a second color. Erase the point names still visible and erase the circle. You may choose to either color the octagonal design inside the pinwheel, or you may choose to erase the unused line segments. Congratulations! You have just constructed a pinwheel!