Download Triangle origami

MATH 212
Spring 2008
Name____________________________________
Origami Constructions: Triangles
Follow these instructions carefully. They are based on the Hands On activity on pp.
670-671 of MR.
The Basic Folds
1. On a blank sheet of white paper, draw a line segment CD; label the endpoints.
Measure its length with a ruler and record it below. Now fold C onto D and make
a crease to produce a line l ; mark the point M where l intersects CD. Measure
€ record the values below. Finally,
the lengths of both segments CM and MD and
using your protractor as accurately as you can, find the exact measure of one of
the angles made between CD and l ? Record it below. Is €l really the
€ of CD?€
perpendicular
€bisector
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2. Use a new sheet of paper to draw an angle made up from two rays with vertex at
a point A; use a straightedge. Measure the angle you have drawn with a
protractor and record it below. Now fold one of the rays onto the other, making a
crease that produces the angle bisector. Then use the protractor to find the exact
measures of both of the angles made between the arms of the angle you drew and
the folded line; record them both below. According to your measures, is the folded
line really a bisector?
3. Use a third sheet of paper for this next item. Draw a bold pencil line and label it
l , then mark a point P not on this line. Fold a strong crease into the paper to
construct the perpendicular line to l that passes through P. Using your
protractor as accurately as you can, what is the exact measure of one of the
angles made between the line l and the folded “perpendicular”? Record it below.
€
€
Exploring Properties of Triangles
1. On a fourth sheet of blank paper, draw a large triangle ABC. Use paper folding
to construct the three angle bisectors of the interior angles of the triangle. What
is interesting about how these three lines intersect?
2. On a fifth sheet of paper, draw a large acute triangle ABC. Use paper folding to
construct the three perpendicular bisectors of the sides of the triangle. What
special property do you observe?
3. Repeat the instructions for #2 above, but for an obtuse triangle. What do you
notice here?
4. If you were to repeat the instructions for #2 with a right triangle, what do you
think would happen? Explain. (You may want to carry out the procedure to verify
your conjecture, but this is not required.)
5. On a seventh sheet of paper, draw a large acute triangle ABC and use paper
folding to construct the three altitudes of the triangle; what do you discover?
What would have happened if the triangle were a right triangle? an obtuse
triangle?
6. On an eight sheet of paper, draw a large acute triangle ABC and make very short
creases to locate the three midpoints of the sides of the triangle; mark these
three points L, M, N. Then use stronger creases to construct the three medians of
the triangle. Does any special phenomenon occur?
Finally, staple all 8 sheets with your origami constructions behind this page and
turn in the whole packet.