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Visual-Dynamic School Geometry
Using Technology for Implementing the 21st Century Pedagogy

  
 
 

Geometry Navigator TM - visual-dynamic plane geometry

 
     

 

   
 

LIST OF LESSONS

Printable Version
 

POINTS, LINES AND ANGLES

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Points and Lines

 

The Concept of a Point in Geometry

 

Lines - Rays - Segments

 

Straight Lines through Three Points

 

The Shortest Path between Two Points

 

Points on a Line

 

Lines and Angles

The Concept of an Angle and Its Measurement

 

The Types of Angles

 

Multiples of the Right Angle

 

Adjacent Supplementary Angles

 

Vertical Angles

 

Shortest Distance from a Point to a Line

 

Parallel and Non-Parallel Lines

Angles Formed by Two Parallel Lines and a Transversal

 

Checking the Parallelism of Lines

 

Parallels and Perpendiculars

 

The Angle Bisector and Its Properties

 

Bisectors of Adjacent Supplementary Angles

 

The Perpendicular Bisector and Its Properties

 

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TRIANGLES

 

General

 

The Sum of Angles of a Triangle

 

Defining Triangles by Their Angles

 

Defining Triangles by Their Sides

 

The Exterior Angles of a Triangle

 

Constructing an Isosceles Triangle and an Equilateral Triangle

 

Relations between Sides and Angles in a Triangle

 

Constructing a Triangle from Three Given Segments

 

The Altitude of a Triangle

 

The Pythagorean Theorem and Its Graphic Representation

 

The Area of a Triangle

 

The Area of a Right-Angled Triangle

 

The Area of an Acute Triangle

 

The Area of an Obtuse Triangle

 

The Area of a Triangle - Summary

 

Congruent Triangles

 

Checking a Congruence - an Example (S.A.S. case)

 

The S.A.S. Congruence Postulate - a Graphical Proof

 

The A.S.A. Congruence Postulate - a Graphical Proof

 

The S.S.S. Congruence Postulate

 

The S.S.S. Congruence Postulate - a Graphical Proof

 

The S.S.A. Congruence Postulate - a Graphical Proof

 

The Congruence Postulates - Summary

 

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Similar Triangles

 

Proportional Segments and the Concept of Similarity

 

The Intercept Theorem

 

The A.A.A. Similarity Criteria

 

Parallel Sides in Similar Triangles

 

Creating Similar Triangles with Parallel Lines

 

The S.A.S. Similarity Criteria

 

The S.S.S. Similarity Criteria

 

The Areas of Similar Triangles

 

Angle Bisectors and Inscribed Circles of Similar Triangles

 

Circumscribed Circles of Similar Triangles

 

Medians of Similar Triangles

 

Special Segments

 

Angle Bisectors

 

Perpendicular Bisectors

 

Medians

 

Altitudes

 

Location of the Special Points in Different Triangles

 

Four Special Points in an Equilateral Triangle

 

The Sum of Distances from Inside Point to the Sides

 

Areas of Shapes Formed by Connecting Middle Points

 

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POLYGONS

 

Quadrilaterals

 

A Rectangle and Its Properties

 

A Square and Its Properties

 

A Parallelogram and Its Properties

 

Transformation: Parallelogram - Rectangle - Square

 

A Rhombus and Its Properties

 

Transformation: Parallelogram - Rhombus - Square

 

A Kite and Its Properties

 

The Sum of Interior Angles of Any Quadrilateral

 

Other Polygons

 

Regular and Non-Regular Polygons

 

The Interior Angle of a Regular Polygon

 

The Sum of Interior Angles of Any Polygon

 

The Exterior Angle of a Regular Polygon

 

The Sum of Exterior Angles of Any Polygon

 

Similar Polygons

 

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CIRCLES

 

Angles, Chords, Tangents

 

An Inscribed Angle

 

Central Angles, arcs and Chords

 

Chords and Angles

 

A Semicircle Angle

 

Chords and Their Relation to the Circle Center

 

Intersecting Chords

 

A Tangent to a Circle and Its Properties

 

The Angle Between a Chord and a Tangent

 

A Tangent and a Secant Intersecting Outside a Circle

 

The Angle Between Two Secants

 

Common Tangents of Two Circles

 

The Line of Centers of Two Intersecting Circles

 

The Mutual Position of Two Circles and the Common Tangents

 

External Tangents of Non-Intersecting Circles

 

Internal Tangents of Non-Intersecting Circles

 

Circumscribed and Inscribed Circles

 

The Circumscribed Circle of a Triangle

 

The Inscribed Circle of a Triangle

 

Circles and Different Types of Triangles

 

Inscribed Quadrilaterals and Their Properties

 

Circumscribed Quadrilaterals and Their Properties

 

Circumscribed Circles and Different Quadrilaterals

 

Inscribed Circles and Different Quadrilaterals

 

Circles and Regular Polygons

 

The Interior Angles of a Regular Polygon

 

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CONSTRUCTIONS

 

Basic Constructions

 

An Angle Equal to a Given One

 

The Bisector of an Angle

 

The Perpendicular Bisector of a Segment  

 

A Perpendicular to a Line through an External Point

 

A Parallel to a Line Through an External point

 

A Parallel to a Line Through an External Point (2)

 

Dividing a Segment into a Given Number of Equal Segments

 

Triangles and Quadrilaterals

 

Constructing Special Segments in a Triangle

 

Constructing a Rectangle

 

Constructing a Square

 

Constructing a Parallelogram Given Its Sides' Lengths

 

Constructing a Parallelogram Given Lengths of Two Sides and a Diagonal

 

Constructing a Parallelogram Given Lengths of Two Sides and an Altitude

 

Circles

 

Locating the Center of a Circle

 

Finding the Diameter of a Circle

 

Constructing a Tangent to a Circle

 

Constructing a Tangent to a Circle through an External Point

 

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  Copyright 1995-2015 Dr. Joseph Dalin, All rights reserved.