Proving the Relationship between Delta and Theta in an Isosceles Triangle

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In summary, the conversation is about proving that the angle "delta" of an Iscosles Triangle is equal to 4 times angle "theta"b minus 2 times angle "theta"a. The triangle has two equal angles which are bisected by the radius of a circle, and when the rays of the radius and the two equal sides are extended, they create two equal angles "theta"a. The conversation also mentions the possibility of drawing a diagram to better understand the problem.
  • #1
kahless2005
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Given an Iscosles Triangle with defined angle "delta". The other two angles are equal and bysected by the radius of a circle. Continuing the rays of the radius and two equal length sides of the triangle yields two equal angles "theta"a. I need to show that "delta" = 4*"theta"b - 2*"theta"a.

My work:
I assume that this is supposed to be two rays of light passing through a drop of water without any refraction.

I need to know whether "theta"b is the angle on the other side of "theta"a, or is it the other "half" of the bysected angles.


Its been too long since I've done geometry, and I did not have a good professor
 
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  • #2
You description is rather diffucult to follow.

Could you provide a diagram?
 
  • #3
how do you provide a diagram?
 
  • #4
If you have a scanner, then scan the diagram you were working from. Start a new post (reply to this thread). In the page you then goto, you will be able to upload a file.
If you don't have a scanner, then use a graphics/image editor to draw the diagram, save it, then upload it.
 
  • #5
nevermind, I figured it out... Thanks for the help anyway Fermat!
 

1. What is an isosceles triangle?

An isosceles triangle is a type of triangle that has two sides of equal length. This means that two of the angles in the triangle are also equal. The third side, called the base, may have a different length from the other two sides.

2. How can you identify an isosceles triangle?

An isosceles triangle can be identified by looking for two sides that are the same length and two angles that are the same measure. The angle opposite the base will always be the same as the other two angles.

3. What is the formula for finding the area of an isosceles triangle?

The formula for finding the area of an isosceles triangle is A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle. The height can be found by drawing a perpendicular line from the base to the opposite vertex.

4. Can an isosceles triangle also be a right triangle?

Yes, an isosceles triangle can also be a right triangle. This means that one of the angles in the triangle is a right angle (90 degrees). If the two equal sides are the legs of the right triangle, then the base will be the hypotenuse.

5. What are some real-life applications of isosceles triangles?

Isosceles triangles can be found in many real-life applications, such as in architecture and construction. They are often used in the design of roofs, bridges, and other structures. They can also be found in nature, such as the shape of a sail on a sailboat or the shape of a butterfly's wings.

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