Focicle2020's Fun Proof-O-Pedia

Yehchan Yoo, Jun 10, 2016

In this GeoGebra book, I have gathered up the GeoGebra applets I made in my free time to help others understand the workings of certain mathematical concepts and -- most importantly -- [b]to teach them to have fun with math![/b] I hope that people will enjoy my GeoGebra applets! ;) Title Image Source: [url]https://openclipart.org/detail/245716/carl-gausss-formula-to-quickly-add-up-all-numbers-from-1-to-n[/url]

Table of Contents

  1. Having Fun with Triangles
    1. Rearrangement Proof of the Pythagorean Theorem
    2. Playing with Congruent Triangles
    3. Proof of Angle Bisector Theorem
    4. Triangle Generator (SSS, SAS, ASA)
  2. Circles...Circles...Circles...
    1. Visual Proof for Area of a Circle
  3. Power of a Point Proofs (Olympiad Level)
    1. Power of a Point Proof Part 1: Between Two Chords
    2. Power of a Point Proof Part 2: Between a Tangent and a Secant
    3. Power of a Point Proof Part 3 (Between Two Secants Intersecting Outside the Circle)

1.

Having Fun with Triangles

  • 1. Rearrangement Proof of the Pythagorean Theorem
  • 2. Playing with Congruent Triangles
  • 3. Proof of Angle Bisector Theorem
  • 4. Triangle Generator (SSS, SAS, ASA)

1.1.

Rearrangement Proof of the Pythagorean Theorem

This GeoGebra demonstration will show one of the most famous proofs of Pythagorean Theorem ([math]a^2 + b^2 = c^2[/math]): the rearrangement proof![br][br]This will require a bit of concentration and basic mathematical skills to understand...[b]But, once you understand it, you will see how cool this is![/b][br](Click here if you want to explore through more proofs of the theorem, Here is the link: [url]http://en.wikipedia.org/wiki/Pythagorean_theorem#Proofs[/url])
– Yehchan Yoo

1.2.

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1.3.

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1.4.

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2.

Circles...Circles...Circles...

  • 1. Visual Proof for Area of a Circle

2.1.

Visual Proof for Area of a Circle

A geometric proof of the area of a circle done by unrolling the circle into a triangle. (Can change the size of the given circle if necessary!)[br][br](More about proving the area of a circle: [url=https://en.wikipedia.org/wiki/Area_of_a_disk]https://en.wikipedia.org/wiki/Area_of_a_disk[/url])
– Yehchan Yoo

3.

Power of a Point Proofs (Olympiad Level)

  • 1. Power of a Point Proof Part 1: Between Two Chords
  • 2. Power of a Point Proof Part 2: Between a Tangent and a Secant
  • 3. Power of a Point Proof Part 3 (Between Two Secants Intersecting Outside the Circle)

3.1.

Power of a Point Proof Part 1: Between Two Chords

– Yehchan Yoo

3.2.

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3.3.

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