MATH - Geometry Demo

1. Introduction to Geometry
Definitions • Measuring Angles • Line and Angle Relationships • Triangles Definitions of Figures and Solids • Summary

2.

Construction

Duplicating Segments and Angles • Constructing Perpendicular Bisectors • Constructing Perpendiculars • Constructing Angle Bisectors • Constructing Parallel Lines • Constructing Points of Concurrency • The Centroid • Summary

3.

Lines and Angles

Angle Relationships • Parallel Lines • Midpoint and Slope • Slope of Parallel and Perpendicular Lines • Equations of Lines • Intersections of Lines • Summary

4.

Triangles

Triangles Sum Conjecture • Properties of Isosceles Triangles • Triangle Inequalities • Summary

5.

Congruencies

SSS and SAS Congruencies • ASA Congruencies • SAA Congruencies • Summary

6.

Polygons and Their Properties

Polygon Sum Conjecture • Exterior Angles of a Polygon • Kites and Trapezoids • Mid-segments Parallelograms • Summary

7.

Circles

Definition • Chord Properties • Tangent Properties • Arcs and Angles • Circumference/Diameter Ratio • Arc Length • Summary

8.

Transformations

Transformations • Properties of Isometrics • Symmetry • Summary

9.

Tessellations

Tessellations with Regular Polygons • Tessellations with Non-regular Polygons • Tessellations Using Only Translations • Tessellations and Rotations • Tessellations and Glide Reflections • Summary

10.

Area

Areas of Rectangles and Parallelograms • Areas of Triangles, Trapezoids and Kites • Areas of Regular Polygons • Areas of Circles • Surface Area • Summary

11.

Pythagorean Theorem

The Theorem of Pythagoras • Converse Special Right Triangles • Distance Calculations • Summary

12.

Volume

Polyhedrons, Prisms and Pyramids • Solids with Curved Surfaces • Cylinders • Cones • Summary

13.

Similarity

Similar Triangles • Indirect Measurement with Similar Triangles • Corresponding Parts • Proportions with Area and Volume • Summary

14.

Deductive Reasoning

Symbols of Logic • Modus Tollens, Negation, Law of Syllogism • Law of Contra-positive • Direct Proofs • Conditional Proof • Indirect Proof • Summary

15.

Inductive Reasoning

Definition • Number and Picture Patterns • Finding the nth Term • Mathematical Modeling • Summary

16.

Geometric Proof

Postulates of Geometry • Geometric Proofs • Proving Angle Conjectures • Parallelograms and Parallel Lines Related Proofs • Summary