Question

Proofs of The Pythagorean Theorem

Steven Zheng Steven Zheng posted 10 months ago


Answer

Proof By Area method


Draw three squares using the sides of the right triangle ABC as one of their sides, respectively.


The altitude from the right angle ∠ACB intersects the hypotenuse AB at point J, and the side HI of square ABHI at point K.


Connect point A to G and point C to H


Look at △ABG and △CBH ,

∠ABG =∠CBH = 90° + ∠ABC\kappa

According to the condition of triangles congruent SAS,

△ABG \cong △CBH


In the right trapezoid ABCF,

S_{CBGF} = 2S_{△ABG}

In the right trapezoid CBHK,

S_{BHKJ} = 2S_{△CBH}

\therefore S_{CBGF} =S_{BHKJ}


Similarly,

S_{ACED} = S_{AJKI}

\therefore S_{CBGF} + S_{ACED} = S_{BHKJ} + S_{AJKI} = S_{ABHI}

\therefore a^2+b^2 = c^2

Steven Zheng Steven Zheng posted 10 months ago

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