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If $\overline{D E}$ in the figure below is parallel to $\overline{A B}, \triangle A B C$ will be similar to $\triangle D E C .$ Find $x .$

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Chapter 9

An Introduction to Geometry

Section 5

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So first off, we're told that these two lines here are parallel. Okay, So because they're parallel, all three angles are congruent, meaning that these two triangles we see are similar. So here's the first large triangle and then the second tribal is the smaller a triangle within. So to find X, we're gonna set up a proportion with a corresponding sides. So five corresponds to 12 as X corresponds to 10. Okay, so we can set up, we can cross multiply five times 10 is 50 and this is equal to 12 times x. And if we divide both sides by 12 we find that X is equal. Teoh four and 16

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