How do you do #18 in Test 6 Section 3 without a calculator?

The key to this one is recognizing that you’ve got similar triangles. First, both triangle CDB and triangle CEA contain angle C. The question also tells you that \overline{BD}\parallel\overline{AE}, which means that angle CDB is also a right angle. Therefore, you have angle-angle similarity.

It’s also good to recognize a 6-8-10 triangle quickly. Know your Pythagorean triples! 🙂

From there, all you need to do is recognize that the length of \overline{AE} is 3 times the length of \overline{BD}, which means all the sides of triangle CEA are 3 times the length of their corresponding sides in triangle CDB. Therefore, because the length of \overline{CD} is 10, the length of \overline{CE} must be 30.

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