MHB Prove: (AC)² = (AD)² + (AB)·(CD)

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In trapezoid ABCD, where AB is parallel to CD and AD equals BC, the relationship AC² = AD² + (AB)(CD) needs to be proven. The proof involves applying the properties of trapezoids and the Pythagorean theorem. By constructing perpendiculars from points A and B to line CD, the segments can be analyzed to demonstrate the equality. The geometric relationships and congruencies established in the trapezoid facilitate the proof. This confirms the stated equation holds true under the given conditions.
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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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