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Refer to the similar triangles shown below. See Example 4.

a. Name 3 pairs of congruent angles.b. Complete each proportion.$$\frac{L M}{H J}=\frac{ }{J E} \quad \frac{M R}{J E}=\frac{}{H E} \quad \frac{}{H J}=\frac{L R}{H E}$$c. We can write the answer to part b in a more compact form:$$\frac{L M}{}=\frac{M R}{H}=\frac{}{H E}$$

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a. $\angle L \cong \angle H, \angle M \cong \angle J, \angle R \cong \angle E$b. $M R, L R, L M$c. $H J, J E, L R$

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Chapter 9

An Introduction to Geometry

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Congruent Triangles and Similar Triangles

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all right, we know these two triangles air similar. So let's go ahead and write the congruent, um, corresponding angles. So angle l corresponds to angle age, so we would right angle l is congruent Teoh angle age and then you're going to do the same thing for the other two angles. You'd want to write that angle em is Congress to angled J. And finally, angle are is congruent to angle e. We can, uh, also writes, um, proportions to solve for unknown side ling. So those proportions would be written as, um side length l m l m is to side length. H j was to correspond to each other as, um a side length is corresponding, or is to j e. So that one would be m R. Because that's in the same position as J. E. So m r. So now that we know m r is to j E, what is to h e. So h he is right here. This isn't the relatively same position as all our Swede, right? L r. And so what is to H J? If we go back and find that l m l m is to hj as l R s t e h e weaken. Right. This a more compact by taking. Since we know that these all are corresponding to each other, we can shorten it by picking. Um, l m is to each j l m t h j, and we're gonna set that equal. Teoh m R j e. And so we don't have to repeat that, Marge A e We're gonna find the one that we haven't done yet, which is the l r h e. We're gonna set that equal. So you can say l m is to h J as a Morris to J E as LR is to H.

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