Geometry and trig proofs, with diagrams

In summary: It is still a valid mathematical concept and can be useful in certain situations. Additionally, the definition of a triangle as a shape with three angles greater than 0 is already widely accepted and used in mathematics.
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  • #2
http://www.mathsisfun.com/geometry/degrees.html said:
Why 360 degrees? Probably because old calendars (such as the Persian Calendar) used 360 days for a year - when they watched the stars they saw them revolve around the North Star one degree per day.

I thought that was a fairly interesting statement. If I was a student, I would want my professor to state things like this. Liekwise, if I was a professor, I would introduce things like this to my class.
 
  • #4
I was messing with the triangle on the interactive thing, and made the triangle just a line. It said the line is an obtuse isosceles triangle. Really? Is "obtuse isosceles triangle" really another way to say "a line"?

Edit: I was thinking about this and I think the definition of triangle should be (if it's not already) a shape with 3 angles, each greater than 0.
 
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  • #5
leroyjenkens said:
I was messing with the triangle on the interactive thing, and made the triangle just a line. It said the line is an obtuse isosceles triangle. Really? Is "obtuse isosceles triangle" really another way to say "a line"?

Edit: I was thinking about this and I think the definition of triangle should be (if it's not already) a shape with 3 angles, each greater than 0.

I haven't used this tool, so I can't check what you were looking at. However, in mathematics you will find many examples of what are called "degenerate" forms of familiar objects. Yes, you can flatten a triangle into a straight line and it is still technically a triangle. You can also squash a cube into a flat plane and you can do many other strange things. When first learning the subject, these special cases are just confusing so teachers avoid them. However, they turn out to be important further on in mathematics so it is useful to get comfortable with degenerate cases of geometric and algebraic objects.
 
  • #6
There is also a very good site about geometry:gogeometry.com .the site contains a big number of theoremes as exercises with many question in order to prove the theoreme,
 
  • #7
leroyjenkens said:
I was messing with the triangle on the interactive thing, and made the triangle just a line. It said the line is an obtuse isosceles triangle. Really? Is "obtuse isosceles triangle" really another way to say "a line"?

Edit: I was thinking about this and I think the definition of triangle should be (if it's not already) a shape with 3 angles, each greater than 0.

Why would you want that to be the definition? There is nothing inconsistent or wrong about a degenerate triangle like the one you describe.
 

1. What is the purpose of using diagrams in geometry and trig proofs?

In geometry and trigonometry, diagrams are used to visually represent the given information and relationships between different elements. They help to make the proofs easier to understand and provide a visual aid for problem-solving.

2. How can I effectively use diagrams in my geometry and trig proofs?

When using diagrams in proofs, it is important to label all the elements accurately and clearly. Also, make sure to include all relevant information and use proper notation. You can also use different colors and shapes to highlight important elements and relationships.

3. Can diagrams be used as a substitute for written explanations in proofs?

No, diagrams should not be used as a substitute for written explanations in proofs. They serve as a helpful visual aid, but written explanations are still necessary to fully explain the reasoning and logic behind the proof.

4. Are there any common mistakes to avoid when using diagrams in geometry and trig proofs?

One common mistake is not accurately representing the given information in the diagram. Another mistake is not using proper notation or labeling, which can lead to confusion or incorrect conclusions.

5. How can I improve my skills in using diagrams for geometry and trig proofs?

Practice is key to improving your skills in using diagrams for proofs. Make sure to regularly review and analyze diagrams from different proofs to better understand how they are used to represent relationships and information. You can also seek help from a tutor or teacher for additional guidance.

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