Last question for Jim Thompson Geometry homework

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Explanation:

At the top of the proof, your teacher states "Given" followed by the relevant useful info. We simply repeat that info word for word as statement 1. This is how all proofs start out. We start with what we're given and try to build toward what we want to prove.

So this is why reason 1 is "given". Reason 2 is "given" also. When your teacher gives multiple statements like this, it's handy to break them up into the smallest pieces possible.

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For reason 3, we use the SAS Similarity rule here because we have congruent angles LPN and LNM (both 90 degrees each) and the sides are proportional due to the statement

Notice how statement 3 builds entirely off from what statements 1 and 2 set up.

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