



LIST OF LESSONS 
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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 NonParallel 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 RightAngled 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 NonRegular 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 NonIntersecting Circles


Internal Tangents of NonIntersecting 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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