# Geometry

I. Story of Geometry

II. Notes on Materials
1. Nomenclature
2. Charts
3. Activity cards

III. Congruency, Similarity and Equivalence
1. Metal Insets
2. Constructive Triangles
3. Further Exploration

IV. Lines
1. Kinds of Lines
2. Positions of a straight Line
3. Positions of two lines in the same plane
4. Intersecting lines

V. Angles
1. Kinds of angles
2. Parts of angles
3. Measuring angles
4. Bisecting angles
5. Relationship between angles
6. Sensorial preparation for theorems of angles

VI. Polygons
1. Concept
2. Triangles
4. General Polygons
5. Work with compass and straight edge

VII. Equivalent Figures with Metal Insets
1. Sensorial approach
a. Triangle and rectangle
b. Rhombus and rectangle
c. Triangles
d. Trapezoid and rectangle
e. Decagon and rectangle

2. Reasoning approach – Pythagorean Theorem
a. Introduction
b. Sensorial presentation with isosceles triangle
c. Numerical study with scalene triangle
d. General proof with plate of Euclid’s theorem
e. Pythagorean theorem applied to other regular figures with constructive triangles
f. Euclid’s proof of Pythagorean Theorem

VIII. Area of Plane Figure
1. Concept of Area
2. Measurement
3. Notes on story problems
4. Parallelogram
5. Triangles
6. Square
7. Rhombus
8. Pentagon
9. Decagon
10. Formulas with metal insets of equivalent figures

IX. The Circle
1. Nomenclature
2. Relationship between circle and straight line
3. Relationship between two circles
4. Circle as a regular polygon
5. Circumference
6. Area
7. Apothem and side of a regular polygon

X. Solids
1. Review of nomenclature
2. Basic concepts
3. Cross sections
4. Volume
5. Volume of non-rectangular prisms
6. Polyhedrons
7. Solids of rotation
8. Surfaces of solids

XI. Measurement
1. Length
2. Volume
3. Temperature
4. Mass
5. Force
6. Time
7. Relationships Between Units4