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

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SUMMARY

The discussion focuses on proving that rectangle ABCD and square BFGH have equal areas. It is established that BE equals BC, which is a critical relationship for the proof. The approach involves using trigonometric identities, specifically that if x = sin(a), then b = 1 - cos(a), to derive the necessary area equivalence. The proof requires completing the circle and extending line BF through the completed circle.

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  • Understanding of basic geometry concepts, specifically properties of rectangles and squares.
  • Familiarity with trigonometric functions and identities, particularly sine and cosine.
  • Knowledge of circle geometry, including diameters and chord properties.
  • Ability to manipulate algebraic expressions and geometric proofs.
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  • Study the properties of rectangles and squares in geometry.
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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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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:
prove that measure x equals the square root of a times b. complete the circle and extend line BF through the completed circle.
 

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