Geometry: a guide for teachers

Machine generated contents note: ch. 1 Seminar 1: Polygons in the Plane

Preface. To the Seminar Leaders

1. Definition of a Polygon

2. Classification of Triangles

3. Classification of Quadrilaterals

4. Congruence

5. Angles: A Review and Some Remarks

6. Angles and Parallel Lines

7. Homework

ch. 2 Seminar 2: More Fundamentals of Plane Geometry

1. Interior Angles of Polygons

2. Pythagorean Theorem

3. Distance Between Points in the Plane

4. Definition of a Circle

5. Interesting Classroom Activity on Circles

6. Homework

ch. 3 Seminar 3: Tessellation

1. Introduction

2. Tessellating with Triangles

3. Why Discuss Tessellation in the Classroom?

4. Tessellation with Quadrilaterals

5. Tessellation with Pentagons

6. Pentagons, Hexagons and n-gons with n>6.

7. Homework

8. References

ch. 4 Seminar 4: Regular Polygons and Regular Polyhedra

1. Construction of a regular 3-gon, 4-gon, 5-gon and 6-gon

2. Five Regular Polyhedra

3. Homework

4. Pentagon Construction Proof (Optional)

ch. 5 Seminar 5: Symmetry

1. Symmetries of an Equilateral Triangle

2. Arithmetic of the Symmetries of the Equilateral Triangle

3. Representing Symmetries by Permutations

4. Symmetries of a Square

5. Representing Symmetries by Permutations

6. Homework

ch. 6 Seminar 6: Lattice Polygons

1. Introduction to Lattice Polygons

2. Lattice Squares

3. Which Positive Integers Are Sums of Two Squares?

4. Homework

ch. 7 Seminar 7: The Area of Polygonal Regions

1. Properties of the Area of a Polygonal Region

2. Area of Rectangular and Triangular Regions

3. Area of Other 4-sided Regions

4. Area of Other Polygonal Regions

5. Area of the Region in a Lattice Polygon

6. Homework

ch. 8 Seminar 8: The Area of a Disk and Disk Packing

1. Introduction

2. Disk Packing Activity I

3. Area of a Disk

4. Disk Packing Activity II

5. Density of Packings on the Entire Plane

6. Homework

ch. 9 Seminar 9: Dissection

1. Introduction to Dissection

2. Dissection of any Parallelogram into a Rectangle of the Same Base Length and Height

3. Dissection of any Rectangle into any other Rectangle of the Same Area, an Example

4. (Optional) Dissection of an Arbitrary Rectangle into any other Rectangle of the Same Area

5. Dissection of Polygons of the Same Area

6. Homework

ch. 10 Seminar 10: Geometry in Three Dimensions

1. Points, Lines and Planes in R3

2. Coordinates in 3-space

3. Prisms and Pyramids

4. Volume of Prisms and Pyramids

5. Homework.