Session 2: Folding to Construct Shapes
Use a pen or marker, a straightedge (if you use a ruler as your straightedge do not
measure!), and patty paper to complete the constructions described in the
problems below. You can fold the patty paper to create creases, and since you can
see through the paper, you can use the folds to construct geometric objects.
1. Draw a line segment on the patty paper, making sure the line segment is not
parallel to the edges of the paper.
a) Construct a line that is a perpendicular bisector to your original segment.
i. Describe your construction method.
ii. How do you know your new line is a perpendicular bisector?
b) Construct a line that is parallel to your original segment.
i. Describe your construction method.
ii. How do you know your new line is parallel to your original segment?
Fostering Geometric Thinking Field Test 2006-2007
©2006 Education Development Center, Inc.
Draft – Do not reproduce without permission
2. For each of the following, start with a freshly drawn segment on a clean piece
of patty paper. Then construct the shape.
a) a square, with your segment as one of its sides
i. Describe your construction method in pictures and words.
ii. Before you tried your method, why did you think it would work?
iii. Were there methods you tried that didn’t work? What were those
methods?
iv. What are the properties of a square? How do you know your shape
has each of these properties?
b) an isosceles triangle, with your segment as one of the two equal sides
c) an isosceles triangle, with your segment as the base
d) an equilateral triangle, with your segment as one of its sides
Fostering Geometric Thinking Field Test 2006-2007
©2006 Education Development Center, Inc.
Draft – Do not reproduce without permission
e) choose one of the triangles you just constructed and answer the following
i. Describe your construction method in pictures and words.
ii. Before you tried your method, why did you think it would work?
iii. Were there methods you tried that didn’t work? What were those
methods?
iv. What are the properties of this type of triangle? How do you know
your shape has each of these properties?
Fostering Geometric Thinking Field Test 2006-2007
©2006 Education Development Center, Inc.
Draft – Do not reproduce without permission