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# 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 GLv 71 decade agoFavorite 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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