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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
(Runtime 13 minutes / Prerequisite None )

Notational Geometry
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3010 Introduction to Angles
(Runtime 15 minutes / Prerequisite SHOW 3005 )

Detailed Description of Angles
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3015 Exploring Angles
(Runtime 19 minutes / Prerequisite SHOW 3010 )

The Relationship of Angles
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3020 Angle Conversion
(Runtime 15 minutes / Prerequisite SHOW 3015 )

Degrees & Radians
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3025 Common Formulas
(Runtime 13 minutes / Prerequisite SHOW 3020 )

Perimeter, Circumference, Area and Volume
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3030 The Geometric Plane
(Runtime 9 minutes / Prerequisite SHOW 3025 )

Review of the Cartesian Coordinates
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3035 The Pythagorean Theorem
(Runtime 12 minutes / Prerequisite SHOW 3030 )

Alternative Formulas and Examples
(24 Hours Viewing-Window)

CHAPTER 2 - Reasoning
       
Lesson Icon SHOW 3050 Visual Patterns
(Runtime 11 minutes / Prerequisite SHOW 3035 )

Exploring Visual Patterns
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3055 Numeric Patterns
(Runtime 19 minutes / Prerequisite SHOW 3050 )

The Pascal Triangle and Its Properties
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3060 Logic
(Runtime 10 minutes / Prerequisite SHOW 3055 )

Deductive and Inductive Reasoning
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3065 Set-Theory
(Runtime 17 minutes / Prerequisite SHOW 3060 )

Review
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3070 Truth Table
(Runtime 19 minutes / Prerequisite SHOW 3065 )

The Logical Operands
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3075 Biconditional Statements
(Runtime 10 minutes / Prerequisite SHOW 3070 )

Properties & Negation
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3080 Logic Properties
(Runtime 14 minutes / Prerequisite SHOW 3075 )

The Algebra of Logic
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3085 If-Then Statements
(Runtime 14 minutes / Prerequisite SHOW 3080 )

Implication, Converse, Inverse and Contra-Positive Forms explained
(24 Hours Viewing-Window)

CHAPTER 3 - Lines
       
Lesson Icon SHOW 3100 Parallel & Transversal Lines
(Runtime 17 minutes / Prerequisite SHOW 3085 )

Derived Properties and Proof
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3105 Midpoint of Line Segments
(Runtime 15 minutes / Prerequisite SHOW 3100 )

Coordinates of the Midpoint
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3110 The Length of Line Segments
(Runtime 11 minutes / Prerequisite SHOW 3105 )

Distance Between Points
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3115 Slope of the Line
(Runtime 12 minutes / Prerequisite SHOW 3110 )

Computing the Slope
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3120 Deriving the Linear Equation
(Runtime 20 minutes / Prerequisite SHOW 3115 )

The Slope Intercept Form
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3125 The X & Y Intercept
(Runtime 15 minutes / Prerequisite SHOW 3120 )

Drawing the Line
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3130 Perpendicular Lines
(Runtime 17 minutes / Prerequisite SHOW 3125 )

The Characteristics of Perpendicular Lines
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3135 Parallel Lines
(Runtime 14 minutes / Prerequisite SHOW 3130 )

The Characteristics of Parallel Lines
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3140 Intersecting Lines
(Runtime 11 minutes / Prerequisite SHOW 3135 )

The Characteristics of Intersecting Lines
(24 Hours Viewing-Window)

CHAPTER 4 - Polygons
       
Lesson Icon SHOW 3200 Introduction to Polygons
(Runtime 21 minutes / Prerequisite SHOW 3140 )

The Anatomy of Polygons
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3205 Triangles
(Runtime 13 minutes / Prerequisite SHOW 3200 )

The Polygon with 3 Sides
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3210 Congruent Triangles
(Runtime 12 minutes / Prerequisite SHOW 3205 )

Translation, Rotation and Reflection
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3215 Proving Triangle Congruency
(Runtime 17 minutes / Prerequisite SHOW 3210 )

Methods: S.S.S., S.A.S., A.S.A. and A.A.S.
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3220 Special Right Triangles
(Runtime 13 minutes / Prerequisite SHOW 3215 )

The "30/60" - "45/45" - "37/53" Applications
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3225 Quadrilaterals I
(Runtime 14 minutes / Prerequisite SHOW 3220 )

The Square and The Rhombus
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3230 Quadrilaterals II
(Runtime 14 minutes / Prerequisite SHOW 3225 )

The Rectangle and The Parallelogram
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3235 Quadrilaterals III
(Runtime 15 minutes / Prerequisite SHOW 3230 )

The Trapezoid and The Kite
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3240 Polygons in the Geometric Plane
(Runtime 24 minutes / Prerequisite SHOW 3235 )

Mapping and Proving Polygons
(24 Hours Viewing-Window)

CHAPTER 5 - Transformation
       
Lesson Icon SHOW 3270 Tessellation
(Runtime 13 minutes / Prerequisite SHOW 3240 )

Patterns in Polygons
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3275 Scale & Proportion
(Runtime 10 minutes / Prerequisite SHOW 3270 )

Scaled Models and the Proportion Principle
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3280 Geometric Translation
(Runtime 10 minutes / Prerequisite SHOW 3275 )

Up, Right, Down and Left Mapping
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3285 Geometric Reflection
(Runtime 10 minutes / Prerequisite SHOW 3280 )

Lines of Symmetry & Object Reflection
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3290 Geometric Rotation
(Runtime 10 minutes / Prerequisite SHOW 3285 )

The Center & Angles of Rotation
(24 Hours Viewing-Window)
       
Lesson Icon SHOW 3295 Geometric Dilation
(Runtime 13 minutes / Prerequisite SHOW 3290 )

Center of Dilation and Scale-Factor K
(24 Hours Viewing-Window)

CHAPTER 6 - Solids
       
Lesson Icon SHOW 3300 Introduction to Solid Geometry
(Runtime 8 minutes / Prerequisite SHOW 3295 )

The Geometry of Solids
(24 Hours Viewing-Window)



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