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# similar triangles

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In the diagram below, DE is parallel to BC, AD = 2, BD = 6, and AE = 10.  Determine the length of EC.

Mar 16, 2021

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because DE and BC are parallel, we can determine that triangles ADE and ABC are similar (all three of their angles are equal).

now, we can use similar triangle ratios to find the length of EC.

$$\frac{AD}{AD+BD} = \frac{AE}{AE+EC}$$

$$\frac{2}{8} = \frac{10}{10+EC}$$

$$\frac14 = \frac{10}{10+EC}$$

$$40 = 10+EC$$ (cross multiplied)

$$30 = EC$$

hopefully you can follow what i did there! if you have any further questions, don't hesitate to ask! :)

Mar 16, 2021