Can I Prove That Rectangle ABCD and Square BFGH Have the Same Area?

  • Thread starter DEMJR
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In summary, we are given a rectangle ABCD and a square BFGH, with AE as the diameter of the circle. We want to prove that ABCD and BFGH have the same area. The only given information is that BE = BC. To prove this, we can complete the circle and extend line BF through it.
  • #1
DEMJR
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We are given that ABCD is a rectangle and AE is the diameter of the circle, and BFGH is a square. I want to figure out how to show that ABCD has the same area as BFGH. Where do I even begin? (see attached picture)
 

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  • #2
DEMJR said:
We are given that ABCD is a rectangle and AE is the diameter of the circle, and BFGH is a square. I want to figure out how to show that ABCD has the same area as BFGH. Where do I even begin? (see attached picture)

The only thing you have to go on is the BE equals BC.

Note that if x = sin(a) then b = 1 - cos(a)
 
Last edited:
  • #3
prove that measure x equals the square root of a times b. complete the circle and extend line BF through the completed circle.
 

What is "Prop. 14 II Euclid Question"?

"Prop. 14 II Euclid Question" refers to a proposition on the Euclidean algorithm, which is a method for finding the greatest common divisor of two integers. This particular proposition states that if a number is a multiple of two other numbers, then it is also a multiple of their greatest common divisor.

Who proposed "Prop. 14 II Euclid Question"?

The proposition was proposed by the ancient Greek mathematician Euclid in his book "The Elements".

Why is "Prop. 14 II Euclid Question" important?

This proposition is important because it is a fundamental concept in number theory and has applications in various fields, including cryptography and computer science.

What is the significance of "14 II" in "Prop. 14 II Euclid Question"?

The "14 II" refers to the proposition number in Euclid's book "The Elements". In this case, it is the 14th proposition in the second book of the series.

How does "Prop. 14 II Euclid Question" relate to the Euclidean algorithm?

This proposition is a key step in the proof of the Euclidean algorithm. It helps to establish the algorithm's validity and its ability to find the greatest common divisor of two numbers.

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