The Basics
Points, Line, and Planes
Ruler Postulate and the Segment Addition Postulate
Segment Midpoint and Segment Perpendicular Bisector
Angle Basics
Animation: Types of Angles
Animation: Measuring Angles with a Protractor
Angle Relationships and Types of Triangles
Similar Triangles and Polygons
Congruent and Similar Triangles
The Pythagorean Theorem
The Pythagorean Theorem and the Converse of the Pythagorean Theorem
Animation: The Sum of the Interior Angles of a Triangle
Complementary, Supplementary, and Vertical Angles
Angle Bisector
Bisector and Midpoint Exercises - Example 1
Bisector and Midpoint Exercises - Example 2
Ex: Midpoint of a Segment
Ex: Find the Endpoint of a Segment Given the Midpoint and One Endpoint
Introduction to Polygons
Classifying Polygons
Interior and Exterior Angles of a Polygon
Introduction to Proof
Inductive Reasoning
Introduction to Deductive Reasoning
Introduction to Proof Using Properties of Equality
Introduction to Proof Using Properties of Congruence
Parallel and Perpendicular Lines
Parallel and Perpendicular Lines and Planes
Parallel Line Postulate
Perpendicular Line Postulate
Angles and Transversals
Properties of Parallel Lines
Proof: Alternate Interior Angles Are Congruent
Proof: Consecutive Interior Angles Are Supplementary
Proof: Parallel Planes Cut by a Plane Forming Parallel Lines
Proof: Two lines Parallel to a Third are Parallel
Example 1: Parallel Line Properties
Example 2: Parallel Line Properties
Proof: Involving Two Pair of Parallel Lines
Parallel Lines Cut by a Transversal
Corresponding Angle Converse
Proof: Alternate Interior Angles Converse
Proof: Alternate Exterior Angles Converse
Proof: Consecutive Interior Angles Converse
Properties of Perpendicular Lines: Proof 1, Proof 2, Proof 3
Perpendicular Transversals of Parallel Lines
Examples 1: Perpendicular Transversals
Examples 2: Perpendicular Transversals
Perpendicular Bisector of a Segment on the Coordinate Plane
The Distance Formula
Determining the Shortest Distance Between a Line and a Point
Determining the Distance Between Two Parallel Lines
Triangles and Congruence
Proving the Triangle Sum Theorem
Introduction to the Interior and Exterior Angles of a Triangle
Proof: The Sum of the Exterior Angles of a Triangle is 360 Degrees
Proof: The Exterior Angles Theorem
How to Construct an Isosceles Triangle
Proof: The Isosceles Triangle Theorem
Examples: Using the Properties of Isosceles Triangles to Determine Values
Introduction to Congruent Triangles
Hypotenuse - Leg Congruence Theorem
Determining If Two Triangles are Congruent
Example 1: Prove Two Triangles are Congruent
Example 2: Prove Two Triangles are Congruent
How to Construct an Equilateral Triangle
Proof: The Equilateral Triangle Theorem
Examples: Using the Properties of Equilateral Triangles to Determine Values
Relationships with Triangles
Introduction to the Midsegments of a Triangle
Examples: Determining Unknown Values Using Properties of the Midsegment of a Triangle
Introduction and Construction of the Perpendicular Bisectors of the Sides of a Triangle
Proof: Perpendicular Bisector Theorem
Proof: Perpendicular Bisector Theorem Converse
Examples: Determining Values Using the Properties of the Perpendicular Bisectors of a Triangle
Constructing a Perpendicular Bisector Using Geometer's Sketchpad
Introduction to Angle Bisectors of a Triangle
Proof: The Angle Bisector Theorem
Proof: The Angle Bisector Theorem Converse
Constructing the Angle Bisectors of a Triangle
Constructing an Angle Bisector Using Geometer's Sketchpad
Examples: Solving For Unknown Values Using Properties of Angle Bisectors
The Medians of a Triangle
Examples: Using the Properties of the Medians of a Triangle to Solve for Unknown Values
The Altitudes of a Triangle
Constructing the Altitude of a Triangle
Constructing the Altitude of a Triangle Using Geometer's Sketchpad
Proof: The Angle of a Triangle Opposite the Longest Side is the Largest Angle
Triangle Inequality Theorem
Introduction to Indirect Proof
Similarity
Ratios
Rates and Unit Rates
Proportions
Proportion Applications
Unit Scale
Scale Factor
Similar Triangles Using Angle-Angle
Similar Triangles Using Side-Side-Side and Side-Angle-Side
Indirect Measurement Using Similar Triangles
Solving for Unknown Values Using the Properties of Similar Triangles
The Triangle Proportionality Theorem
Using the Properties of the Triangle Proportionality Theorem to Solve for Unknown Values
The Triangle Angle Bisector Theorem
Using the Properties of the Triangle Angle Bisector Theorem to Determine Unknown Values
Circles
Introduction to Circles
Ex: Write the Standard Form of a Circle From a Graph
Ex: Graph a Circle in Standard Form
Ex 1: Write the General Equation of a Circle in Standard Form
Ex 2: Write the General Equation of a Circle in Standard Form (Fractions)
Ex 3: Write General Equation of a Circle in Standard Form (Coefficent Not 1)
Ex 4: Write General Equation of a Circle in Standard Form (Coefficent Not 1 and Fractions)
Ex: Find Standard Equation of a Circle Given Center and Point on the Circle
Ex 1: Find Standard Equation of a Circle Given the Endpoints of a Diameter
Ex 2: Find Standard Equation of a Circle Given the Endpoints of a Diameter
Tangent Lines to a Circle Proof
Tangent Lines to a Circle Example Problems
Prove Tangents Segments to a Circle from a Point are Congruent
Tangent Segments to a Circle Example Problems
Logic
If-Then Statements and Converses
The Converse, Contrapositive, and Inverse of an If-Then Statement
Truth Tables for Compound Statements
Truth Tables for Conditional Statements
Truth Table for the Biconditional Statement
Truth Tables: Showing Statements are Equivalent
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