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

Ex 1: Find the Length of a Side of a Triangle Using Similar Triangles

Ex 2: Find the Length of a Side of a Triangle Using Similar Triangles (Overlapping)

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

Ex: Find the Measure of an Interior Angle of a Triangle Using an Exterior Angle

Ex 1: Find the Measure of an Interior Angle of a Triangle

Ex 2: Find the Measure of an Interior Angle 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

Ex: Find the Measure of an Interior Angle of a Quadrilateral

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