Honors GeometryPage 1

Unit 13

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.
  1. Make a mark on the edge of the circle with a pencil.
  1. Fold the circle so that the mark on the edge touches the center dot. The crease is a chord.
  1. 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.
  1. 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.
  1. Find the midpoint of one side of the triangle by folding that side in half and pinching it. Unfold.
  1. Fold the opposite vertex to the midpoint. Discuss trapezoid, isosceles trapezoid, polygon, parallel and intersecting lines, acute and obtuse angles.
  1. The trapezoid is divided into three equilateral triangles. Fold one of the equilateral triangles over the center triangle. Discuss rhombus, parallelogram, and quadrilateral.
  1. 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.
  1. 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.
  1. Open the figure to the original large triangle.
  1. Fold each vertex to the center dot and crease. Discuss hexagon and regular polygon.
  1. 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?
  1. 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.
  1. 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.
  1. 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.

DO NOT TRACE THE SHAPES!

Rosemary Circle.docMiss Jo Ann Fricker

Lower Moreland HS

Honors GeometryPage 1

Unit 13

Convex Quadrilaterals

Rosemary Circle.docMiss Jo Ann Fricker

Lower Moreland HS

Honors GeometryPage 1

Unit 13

Concave Quadrilaterals


Rosemary Circle.docMiss Jo Ann Fricker

Lower Moreland HS

Honors GeometryPage 1

Unit 13

Rosemary Circle.docMiss Jo Ann Fricker

Lower Moreland HS