CC Geometry
Table of Contents
- Intro to Geometry
- Transformations
- Lines and Angles
- Triangles
- Quadrilaterals
- Similarity & Dilations
- Right Triangles & Trigonometry
- Special Right Triangles Investigation
- Area & Volume
- Area of Circles
- Coordinate Geometry
- Circles
- Thales' Theorem
- Chord Properties 1
- Chord Properties 2
- Chord Properties 3
- Cyclic Quadrilaterals 1
- Cyclic Quadrilaterals 2
- Arcs, Angles and Chords Theorem 1
- Arcs, Angles and Chords Theorem 2
- Arcs, Angles and Chords Theorem 3
- Arcs, Angles and Chords Theorem 4
- Tangent Properties 1
- Tangent Properties 2
- Tangent Properties 3
- Tangent Properties 4
- Tangent Properties 5
Special Right Triangles Investigation
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For t = 45 degrees, record the lengths for sides b and c as you move the slider for a. When you are done, move the slider for t to 60 degrees and record the side lengths for b and c. |
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1. How do the legs of the 45 degree triangle relate to each other? 2. How does the hypotenuse of the 45 degree triangle relate to the legs? 3. How does the longer leg of the 60 degree triangle relate to the shorter leg? 4. How does the hypotenuse of the 60 degree triangle relate to the shorter leg? |
Area of Circles
What is the area of a circle? Explore with the following applet.
Anthony Or, GeoGebra Institute of Hong Kong.
Thales' Theorem
Thales of Miletus is often considered the first great Greek mathematician. He seems to be the beneficiary of history's first attribution: "Hey, this is Thales' theorem." See a biography at MacTutor: [url]http://www-history.mcs.st-and.ac.uk/Mathematicians/Thales.html[/url][br][br]What he noticed and proved concerned a connection between right triangles and circles. What do you notice?[br][br]Why is it true?[br][br]Could you prove it's always true? Thales' proof seems to have used that the sum of the angle measures in a triangle are equal to two right angles. (What we call 180 degrees, nowadays.)
More GeoGebra at [url]mathhombre.blogspot.com[/url].