Course Content
Performing Transformations
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Intro to Euclidean Geometry: Performing Transformations
Intor to Euclidean Geometry Quiz
Intro to Rigid Transformations
Rigid Transformations Quiz
Translations
Translations Quiz
Rotations
Rotations Quiz
Reflections
Reflections Quiz
Dilations
Dilations Quiz
Unit 1 Summary
Transformation Properties and Proofs
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Rigid Transformations
Rigid Transformations Quiz
Dilation Preserved Properties
Dilations Preserved Properties Quiz
Properties & Definitions of Transformations
Properties & Definitions of Transformations Quiz
Symmetry
Symmetry Quiz
Proof with Transformations
Proof with Transformations Quiz
Unit 2 Summary
Congruence
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Transformations & Congruence
Transformations & Congruence Quiz
Triangle Congruence from Transformations
Triangle Congruence Quiz
Congruent Triangles
Congruent Triangles Quiz
Theorems Concerning Triangle Properties
Triangle Theorems Quiz
Working with Triangles
Working with Triangles Quiz
Theorems Concerning Quadrilateral Properties
Quadrilateral Theorems Quiz
Proofs of General Theorems
Proofs Quiz
Constructing Lines & Angles
Constructing Lines & Angles Quiz
Unit 3 Summary
Similarity
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Definitions of Similarity
Definition of Similarity Quiz
Intro to Triangle Similarity
Triangle Similarity Quiz
Solving Similar Triangles
Solving Similar Triangles Quiz
Angle Bisector Theorem
Angle Bisector Theorem Quiz
Solving Problems with Similar & Congruent Triangles
Solving Problems Quiz
Proving Relationships Using Similarity
Proving Relationships Quiz
Solving Modeling Problems with Similar & Congruent Triangles
Modeling Problems Quiz
Unit 4 Summary
Right Triangles & Trigonometry
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Pythagorean Theorem
Pythagorean Theorem Quiz
Pythagorean Theorem Proofs
Pythagorean Theorem Proofs Quiz
Special Right Triangles
Special Right Triangles Quiz
Ratios in Right Triangles
Ratios in Right Triangles Quiz
Intro to the Trigonometric Ratios
Intro to Trig Ratios Quiz
Solving for a Side Using Trig Ratios
Solving for a Side Quiz
Solving for an Angle Using Trig Ratios
Solving for an Angle Quiz
Sine & Cosine of Complementary Angles
Sine & Cosine Quiz
Modeling with Right Triangles
Modeling Problems Quiz
Unit 5 Summary
Analytic Geometry
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Distance and Midpoints
Distance and Midpoints Quiz
Dividing Line Segments
Dividing Line Segments Quiz
Problem Solving with Distance on the Coordinate Plane
Distance Problem Solving Quiz
Parallel & Perpendicular Lines on the Coordinate Plane
Parallel & Perpendicular Lines Quiz
Equations of Parallel & Perpendicular Lines
Equations Quiz
Unit 6 Summary
Conic Sections
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Graphs of Circles Intro
Graphs of Circles Quiz
Standard Equation of a Circle
Standard Equation Quiz
Expanded Equation of a Circle
Expanded Equation Quiz
Unit 7 Summary
Circles
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Circle Basics
Arc Measure
Arc Length from Degress
Intro to Radians
Arc Length from Radians
Sectors of a Circle
Inscribed Angles
Inscribed Shapes
Proofs with Inscribed Shapes
Properties of Tangents
Constructing Regular Polygons Insribed in Circles
Constructing Circumcircles & Incircles
Constructing a Line Tangent to a Circle
Solid Geometry
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2D vs. 3D Objects
Cavalieri’s Principle and Dissection Methods
Volume and Surface Area
Density
Geometry

Pythagorean Theorem Proofs

Explanation

There are many proofs of the Pythagorean Theorem:

  1. Algebraic proof using squares on each side

  2. Geometric proof using rearrangement of triangles

Key idea: The area of the square on the hypotenuse = sum of areas of squares on legs.

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