Honors Geometry
Unit 13
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Rosemary’s Circle
1.
Use a compass to make a circle with a
diameter of 7 inches. Mark the center.
Discuss related geometric terms and
vocabulary such as: plane figure,
circumference, diameter, radius, chord,
center, etc.
2.
Make a mark on the edge of the circle with
a pencil.
3.
Fold the circle so that the mark on the
edge touches the center dot. The crease is
a chord.
4.
Make another fold so that one end of the
crease is at the end of the chord made in
step 3, the edge of the circle touches the
center dot, and the segment is congruent
to the smaller segment made in step 3. the
folded figure now looks like an ice cream
cone.
5.
Make a third fold so that the edge of the
circle touches the center dot and the ends
of the crease touch one endpoint of each of
the other chords. The figure formed is an
equilateral triangle. Discuss area,
perimeter, sides and angles.
6.
Find the midpoint of one side of the
triangle by folding that side in half and
pinching it. Unfold.
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
Page 2
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
7.
Fold the opposite vertex to the midpoint.
Discuss trapezoid, isosceles trapezoid,
polygon, parallel and intersecting lines,
acute and obtuse angles.
8.
The trapezoid is divided into three
equilateral triangles. Fold one of the
equilateral triangles over the center
triangle. Discuss rhombus,
parallelogram, and quadrilateral.
9.
Fold the last triangle over the other two.
Point out that the smaller triangles are
congruent and they are similar to the
larger equilateral triangle.
10.
Set the folded triangles in the palm of your
hand. With a little nudging, it will open to
form a pyramid. Discuss base, vertex,
edge, face, and volume. This pyramid
has a triangle for a base and is therefore
called a triangular pyramid or
tetrahedron.
11.
Open the figure to the original large
triangle.
12.
Fold each vertex to the center dot and
crease. Discuss hexagon and regular
polygon.
Rosemary Circle.doc
Page 3
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
13.
Gently let the side rise; coax the figure to
become a truncated pyramid. How many
faces are there for this shape? What
shapes are the faces?
14.
Open to the large triangle. Fold one vertex
down to the midpoint as in step 7, then
fold back again on the crease from the
hexagon. Repeat for the other two vertices
until you have a six-pointed star.
15.
Refold along existing fold lines to create
different convex polygons. Record your
results on isometric dot paper. There are
10 possible convex polygons. Use a
consistent scale for each of the 10
polygons.
16.
By making back-folds as you did for the
six-pointed star, you can make concave
polygons. Make as many concave
polygons as possible and record your
results. There are 10 possible concave
polygons. Also use the same scale for
these 10 polygons.
Page 4
DO NOT TRACE THE SHAPES!
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
Page 5
Convex Quadrilaterals
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
Page 6
Convex Quadrilaterals
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
Page 7
Concave Quadrilaterals
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
Page 8
Concave Quadrilaterals
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
Page 9
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS
Honors Geometry
Unit 13
Page 10
Rosemary Circle.doc
Miss Jo Ann Fricker
Lower Moreland HS