Perimeter and Area

Introduction to Perimeter and Perimeter Formulas
Area and Perimeter Formulas
Determine the Perimeter and Area of a Square on a Grid
Determine the Perimeter and Area of a Rectangle on a Grid
Determine the Area of a Parallelogram on a Grid
Determine the  Area of a Trapezoid on a Grid
Rectangle Area Application:  Flooring

Perimeter and Area of a Rectangle with Decimals
Ex:  Determine the Area of a Rectangle Involving Whole Numbers
Ex: Find the Area of a Triangle (Whole Number)
Ex:  Area of a Parallelogram (Whole Numbers)
Perimeter and Area of a Parallelogram (Whole Numbers)
Perimeter and Area of a Parallelogram (Decimals)
Ex:  Area of a Trapezoid Using Whole Numbers
Determine the Perimeter and Area of a Trapezoid
Perimeter and Area of a Right Trapezoid

Determine the Area of a Triangle on a Grid
Determine the Area of an Obtuse Triangle on a Grid
Perimeter and Area of a Triangle with Decimals

Perimeter and Area of a Triangle with Mixed NumbersFind the Length of  a Missing Side of a  Right Triangle and Perimeter and Area
Perimeter and Area of a Trapezoid with Decimals
Determine the Perimeter and Area of an Irregular Polygon
Find the Perimeter and Area of a L-Shaped Polygon Using Decimals
Ex:  Find the Area of an L-Shaped Polygon Involving Whole Numbers
Ex:  Area of a Triangle (Whole Numbers)
Ex: Find the Area of a Rectangle Given the Perimeter
Ex:  Area of a Trapezoid Using Mixed Numbers
Ex:  Determine the Area of a Rectangle Using Decimals
Ex:  Determine the Area of an L-shaped Polygon Using Decimals
Ex:  Determine the Area of a Rectangle Using Mixed Numbers
Ex:  Area of a Walkway Around a Rectangle
Ex:  Area of a Triangle Involving Fractions
Where Does the Area Formula For a Circle Come From?
Ex:  Determine the Area of a Circle
Ex:  Find the Area of a Ring or Area Between Two Circles
Ex:  Determine an Area Involving a Rectangle and Circle
Ex: Find the Interior Angles of a Triangle From Expressions For the Angles
Ex: Find the Perimeter of an L-shaped Polygon Involving Whole Numbers
Ex: Find the Area of a Rectangle Given the Perimeter
Ex: Using Decimals To Determine the Perimeter of a L-shaped Polygon
Ex:  Determine the Perimeter of a Rectangle using Mixed Numbers
Ex:  Determine the Circumference of a Circle
Area of a Circle Given the Diameter as  a Decimal
Ex:  Determine Perimeter Involving a Rectangle and Circle
Find the Area Inside a Square and Outside a Circle
Ex: Area of a Polygon by Decomposing Area (Triangle/Rectangle I)
Ex: Area of a Polygon by Decomposing Area (Triangle/Rectangle II)
Find the Area of an Irregular Shape (Semi Circle Plus Triangle)

Volume / Surface Area / Misc

Ex:  Determine the Length of a Missing Side Given the Perimeter
Ex:  Determine Volume of a Cone
Ex: Find the Surface Area of an Open Top Box
Find the Surface Area of an Open Top Box
Find the surface Area of a Cylinder
Find the Surface Area of a Sphere
Ex: Volume of a Pyramid
Volume Between Two Spheres
Volume of the Empty Space in a Cubic Box with a Ball Inside
Determine the Percent of a Volume of a Rectangular Pool (Box)

               
Geometric Applications

Ex: Builder's Level Application - Decimal Addition and Subtraction
Ex: Perimeter Application - Linear Feet of Baseboard Needed for a Room
Ex: Area Application - Area of an Inner Room with a Outer Footing

 

ntroduction to Geometry Basics: Points, Lines, Segments, Planes, Angles, and Polygons

Points, Line, and Planes
Identify and Name a Point, Line, Ray, Segment, and Angle
Determine if a Measurement is 1D, 2D, or 3D
Ruler Postulate and the Segment Addition Postulate
Determine Lengths in Centimeters, Millimeters, and Inches
Segment Midpoint and Segment Perpendicular Bisector
Angle Basics
Name and Classify Types of Angles
Animation:  Types of Angles
Animation:  Measuring Angles with a Protractor
Angle Relationships and Types of Triangles
Name Types of Triangles and Determine a Missing Interior Angle
Properties of Polygons and Quadrilaterals
Similar Triangles and Polygons
Congruent and Similar Triangles
Introduction to Similarity
Discover the Ratios of Sides, Perimeters, and Areas of Similar Polygons
Similar Polygons: Find Missing Area Given the Ratio of Perimeters
Similar Polygons: Find Missing Perimeter Given the Ratio of Areas
Scale Factor, Similar Triangles, and Proportions
Sketch a Similar Polygon Using a Scale Factor of 3
The Pythagorean Theorem
The Pythagorean Theorem and the Converse of the Pythagorean Theorem
Using the Pythagorean to Determine the Length of the Hypotenuse
Solve Applications Using the Pythagorean Theorem  (c only)
Animation:  The Sum of the Interior Angles of a Triangle
Ex 2B: Find the Measure of an Interior Angle of a Triangle
Ex: Find the Interior Angles of a Triangle From Expressions For the Angles
Complementary, Supplementary, and Vertical Angles
Determine the Complement and Supplement of a Given Angle
Determine the Measure of Missing Angles from a Figure
Determine the Measure of Vertical Angles and Angles from a Figure
Ex: Write an Expressions for Complementary Angles and Supplementary Angles (Basic)
Ex: Write Expressions and Determine the Measure of Complementary Angles
Ex: Write Expressions and Determine the Measure of Supplementary 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
Scale Factor, Similar Triangles, and Proportions
Sketch a Similar Polygon Using a Scale Factor of 3
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
Circles and Solids:  Radius, Diameter, and Naming Solids
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

Introduction to Perimeter, Area, Surface Area, and Volume

Introduction to Area
Introduction to Volume
Determine the Perimeter of Various Polygons
The Circumference of a Circle
Rectangle Perimeter Application:  Feet of Fencing Required
Perimeter Application: Perimeter With and Without Edge
Circumference Application:  Determine the Radius
Introduction to Area and Area Formulas
Find the Area of a Shape by Decomposing the Area
Area of a Square and Rectangle Using Decimal
Application: Find the Radius of a Circle Given the Area
Determine the Surface Area of a Cube (Decimals)

Determine the Surface Area of a Rectangular Prism (Whole Numbers)
Introduction to Volume
Determine the Volume of a Cube (Decimals)
Determine the Volume of a Rectangular Prism (Whole Numbers)

Volume of a Cylinder and a Pyramid

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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