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PowerMath - Geometry
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- Subject -
Arithmetic Topic
- Preface -

PURPOSE :


PowerMath Geometry®   is a complete course suitable for Grades 9 on up.   The visual and practical nature of geometric principles involve measurement, deductive reasoning and application representing shape, symmetry and properties of space.   Geometry allows you to learn more about the world around you through surveying, measurement and design, given its numerous applications in nature, engineering, astronomy, arts, robotics and so on.

APPLICATION :


Requiring some basic skills in Algebra, this course combines theory proved by logical reasoning with plenty of examples and illustrations, stressing both the theoretical and computational aspects, in a rigorous representation of traditional topics in Geometry.


For Students, lessons are self-paced and self-learning requiring no instructional intervention.


For Teachers, lessons are content specific and optimal to augment their own classroom lectures.

RECOMMENDATION :


Lesson-Shows were designed to be watched sequentially, to build your mathematical knowledge and confidence incrementally.   Skipping any portion of the course (lessons and/or chapters) is not advised.   We suggest that you start with the very first lesson of the subject (Chapter One - Lesson One), while working your way up.   Your starting-point (depending on your abilities), is when you find a specific lesson content challenging.   Alternatively, match your instructor most recent lecture topic or corresponding part of your textbook, with any lesson Title & Description below.


- Contents -

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Geometry LIB
In PDF Format

- Lessons -

CHAPTER 1 - Basic Concepts
       
Lesson Icon SHOW 3005 The Language of Geometry
Notational Geometry
runtime 13 minutes
requires None
       
Lesson Icon SHOW 3010 Introduction to Angles
Detailed Description of Angles
runtime 15 minutes
requires SHOW 3005
       
Lesson Icon SHOW 3015 Exploring Angles
The Relationship of Angles
runtime 19 minutes
requires SHOW 3010
       
Lesson Icon SHOW 3020 Angle Conversion
Degrees & Radians
runtime 15 minutes
requires SHOW 3015
       
Lesson Icon SHOW 3025 Common Formulas
Perimeter, Circumference, Area and Volume
runtime 13 minutes
requires SHOW 3020
       
Lesson Icon SHOW 3030 The Geometric Plane
Review of the Cartesian Coordinates
runtime 9 minutes
requires SHOW 3025
       
Lesson Icon SHOW 3035 The Pythagorean Theorem
Alternative Formulas and Examples
runtime 12 minutes
requires SHOW 3030

CHAPTER 2 - Reasoning
       
Lesson Icon SHOW 3050 Visual Patterns
Exploring Visual Patterns
runtime 11 minutes
requires SHOW 3035
       
Lesson Icon SHOW 3055 Numeric Patterns
The Pascal Triangle and Its Properties
runtime 19 minutes
requires SHOW 3050
       
Lesson Icon SHOW 3060 Logic
Deductive and Inductive Reasoning
runtime 10 minutes
requires SHOW 3055
       
Lesson Icon SHOW 3065 Set-Theory
Review
runtime 17 minutes
requires SHOW 3060
       
Lesson Icon SHOW 3070 Truth Table
The Logical Operands
runtime 19 minutes
requires SHOW 3065
       
Lesson Icon SHOW 3075 Biconditional Statements
Properties & Negation
runtime 10 minutes
requires SHOW 3070
       
Lesson Icon SHOW 3080 Logic Properties
The Algebra of Logic
runtime 14 minutes
requires SHOW 3075
       
Lesson Icon SHOW 3085 If-Then Statements
Implication, Converse, Inverse and Contra-Positive Forms explained
runtime 14 minutes
requires SHOW 3080

CHAPTER 3 - Lines
       
Lesson Icon SHOW 3100 Parallel & Transversal Lines
Derived Properties and Proof
runtime 17 minutes
requires SHOW 3085
       
Lesson Icon SHOW 3105 Midpoint of Line Segments
Coordinates of the Midpoint
runtime 15 minutes
requires SHOW 3100
       
Lesson Icon SHOW 3110 The Length of Line Segments
Distance Between Points
runtime 11 minutes
requires SHOW 3105
       
Lesson Icon SHOW 3115 Slope of the Line
Computing the Slope
runtime 12 minutes
requires SHOW 3110
       
Lesson Icon SHOW 3120 Deriving the Linear Equation
The Slope Intercept Form
runtime 20 minutes
requires SHOW 3115
       
Lesson Icon SHOW 3125 The X & Y Intercept
Drawing the Line
runtime 15 minutes
requires SHOW 3120
       
Lesson Icon SHOW 3130 Perpendicular Lines
The Characteristics of Perpendicular Lines
runtime 17 minutes
requires SHOW 3125
       
Lesson Icon SHOW 3135 Parallel Lines
The Characteristics of Parallel Lines
runtime 14 minutes
requires SHOW 3130
       
Lesson Icon SHOW 3140 Intersecting Lines
The Characteristics of Intersecting Lines
runtime 11 minutes
requires SHOW 3135

CHAPTER 4 - Polygons
       
Lesson Icon SHOW 3200 Introduction to Polygons
The Anatomy of Polygons
runtime 21 minutes
requires SHOW 3140
       
Lesson Icon SHOW 3205 Triangles
The Polygon with 3 Sides
runtime 13 minutes
requires SHOW 3200
       
Lesson Icon SHOW 3210 Congruent Triangles
Translation, Rotation and Reflection
runtime 12 minutes
requires SHOW 3205
       
Lesson Icon SHOW 3215 Proving Triangle Congruency
Methods: S.S.S., S.A.S., A.S.A. and A.A.S.
runtime 17 minutes
requires SHOW 3210
       
Lesson Icon SHOW 3220 Special Right Triangles
The "30/60" - "45/45" - "37/53" Applications
runtime 13 minutes
requires SHOW 3215
       
Lesson Icon SHOW 3225 Quadrilaterals I
The Square and The Rhombus
runtime 14 minutes
requires SHOW 3220
       
Lesson Icon SHOW 3230 Quadrilaterals II
The Rectangle and The Parallelogram
runtime 14 minutes
requires SHOW 3225
       
Lesson Icon SHOW 3235 Quadrilaterals III
The Trapezoid and The Kite
runtime 15 minutes
requires SHOW 3230
       
Lesson Icon SHOW 3240 Polygons in the Geometric Plane
Mapping and Proving Polygons
runtime 24 minutes
requires SHOW 3235

CHAPTER 5 - Transformation
       
Lesson Icon SHOW 3270 Tessellation
Patterns in Polygons
runtime 13 minutes
requires SHOW 3240
       
Lesson Icon SHOW 3275 Scale & Proportion
Scaled Models and the Proportion Principle
runtime 10 minutes
requires SHOW 3270
       
Lesson Icon SHOW 3280 Geometric Translation
Up, Right, Down and Left Mapping
runtime 10 minutes
requires SHOW 3275
       
Lesson Icon SHOW 3285 Geometric Reflection
Lines of Symmetry & Object Reflection
runtime 10 minutes
requires SHOW 3280
       
Lesson Icon SHOW 3290 Geometric Rotation
The Center & Angles of Rotation
runtime 10 minutes
requires SHOW 3285
       
Lesson Icon SHOW 3295 Geometric Dilation
Center of Dilation and Scale-Factor K
runtime 13 minutes
requires SHOW 3290

CHAPTER 6 - Solids
       
Lesson Icon SHOW 3300 Introduction to Solid Geometry
The Geometry of Solids
runtime 8 minutes
requires SHOW 3295



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