Geometry Help

[k3232x]

 

[stapel]

In case the image doesn't display or isn't clear, this is a synopsis of what I'm seeing:

In the trapezoid ABCD, AB is parallel to DC, and the ratio of the two bases is ABC = 2:5. The two diagonals, DB and CA, intersect in the interior at point E. Determine (a) the ratio AE:EC, and (b) delta-ABC:delta-CDE.

To the poster: The image makes it look like the trapezoid is isocesceles (that is, that the angles ADC and BCD are equal). Should we assume this to be true? Also, what is the meaning of the "delta" notation?

When you reply, please include a listing of the steps you have tried thus far.

Thank you.

Eliz.

 

[k3232x]

The triange symbol isnt suppose to mean 'delta' its just suppose to mean triange.

Also, do not assume any angles are equal or 90 degrees

 

[pka]

Note the similar triangles: \(\displaystyle \Delta ABE \sim \Delta CDE\quad \Rightarrow \quad \frac{{AB}}{{CD}} = \frac{{AE}}{{CE}} = \frac{2}{5}\)

Also note that your b) part is about area.
The common perpendicular thru E to both AB and CD gives the altitudes in ratio (2/5). Therefore the areas are in ratio (4/25)