9th class Geometry help urgent?

In the figure http://thumbnails27.imagebam.com/9464/fc7a1e946385...

Given:

AB || CD

Prove that ∠BAE - ∠DCE = ∠AEC

1 Answer

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  • Ossi G
    Lv 7
    1 decade ago
    Favorite Answer

    Hello

    Elongate BA to intersect EC in C'.

    Now there is the triangle EC'A. And ∠EC'A = ∠ECD.

    In the triangle you have angles ∠AEC', ∠EC'A, and

    ∠EAC' = (180° - ∠BAE).

    The sum of angles in a triangle are 180°, so

    ∠AEC' + ∠EC'A + 180° - ∠BAE = 180°

    ∠AEC' + ∠EC'A - ∠BAE = 0

    and

    ∠AEC' = ∠AEC

    ∠EC'A = ∠DCE,

    so

    ∠AEC + ∠DCE - ∠BAE = 0, or

    ∠BAE - ∠DCE = ∠AEC

    regards

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