AD is perpendicular to BC.p.t. AB square+CD square=BD square+AC square
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see diagram. Use Pythagoras theorem in triangles ABD and ADC.
AD^2 = AB^2 - BD^2 = AC^2 - CD^2
so AB^2 + CD^2 = AC^2 + BD^2
AD^2 = AB^2 - BD^2 = AC^2 - CD^2
so AB^2 + CD^2 = AC^2 + BD^2
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