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detektibgapo
Lv 5
detektibgapo asked in Science & MathematicsMathematics · 1 decade ago

Geometry - ABCDEFGH is a rectangular prism FG=BC. Prove that....?

ABCDEFGH is a rectangular prism in which FG = BC.

Prove that CA*2 + AE*2 = ED*2 + DC*2

I cannot draw the exact figure here but I can describe it.

The top rectangle is EFGH, with E joining F, H joining G, E joining H and F joining G. EF and HG are the longer sides.

The bottom rectangle is ABCD, A joins B, D joins C, A joins D and B joins C. AB and DC are the longer sides

H_____________________G

E____________________F

I

I D_____________________C

I

I

I

A____________________B

1 Answer

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  • Shy
    Lv 6
    1 decade ago
    Favorite Answer

    Hi Detektibgapo

    In your figure

    CA*2 + AE*2 = EC^2 (by Pythagoras theorem)

    and

    ED*2 + DC*2 + EC^2 (by Pythagoras theorem)

    So

    CA*2 + AE*2 = ED*2 + DC*2

    Shy

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