Prove: (AC)² = (AD)² + (AB)·(CD)

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SUMMARY

The discussion centers on proving the geometric identity for trapezoid ABCD, where AB is parallel to CD and AD equals BC. The formula to be proven is \(AC^2 = AD^2 + (AB) \cdot (CD)\). Participants emphasize the importance of understanding trapezoidal properties and the Pythagorean theorem in establishing this relationship. The proof relies on the congruence of triangles formed within the trapezoid.

PREREQUISITES
  • Understanding of trapezoidal properties and definitions
  • Knowledge of the Pythagorean theorem
  • Familiarity with geometric proofs and congruence
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the properties of trapezoids in Euclidean geometry
  • Learn about triangle congruence criteria (SSS, SAS, ASA)
  • Explore geometric proof techniques and strategies
  • Investigate applications of the Pythagorean theorem in various geometric contexts
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Students of geometry, mathematics educators, and anyone interested in mastering geometric proofs and properties of trapezoids.

Albert1
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A trapezoid ABCD ,AB//CD ,AD=BC

Prove :

$AC^2=AD^2+(AB).(CD)$
 
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Re: Prove :AC^2=AD^2+(AB).(CD)

Albert said:
A trapezoid ABCD ,AB//CD ,AD=BC

Prove :

$AC^2=AD^2+(AB).(CD)$

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