Reason 1: Given
We basically just restate the given information exactly word for word (symbol for symbol). It may seem redundant, but imagine this proof is something you give to your friend. So you want the proof to be independent and on its own.
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Reason 2: Addition Property of Equality
We're adding [tex]m \angle MON[/tex] to both sides of the first equation mentioned in statement 1.
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Reason 3: Substitution
The [tex]m\angle MON[/tex] on the right hand side is replaced with [tex]m\angle IKH[/tex]. This replacement is valid because of the second equation in statement 1.
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Reason 4: Angle Addition Postulate
This is the idea where we can glue two smaller angles to form a larger angle. Or we can go in reverse to break up a large angle into smaller pieces. This is similar to the segment addition postulate.
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Reason 5: Substitution
Statement 3 says that LOM+MON = JKI+IKH. Statement 4 says LOM+MON = LON. So this must mean LON = JKI+IKH. Then we use another substitution to say LON = HKJ
