SOLUTION: I don't understand proofs. For example: Given: Segment AB is congruent to segment TP. Prove: Segment AT is congruent to segment BP. There is a line image accompanying it. <---

Question 663868: I don't understand proofs. For example:
Given: Segment AB is congruent to segment TP.
Prove: Segment AT is congruent to segment BP.
There is a line image accompanying it.
<---a--b--------t--p--->
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Notice how AP = AT + TP and AP = AB + BP

Since AB = TP (given), this means

AP = AT + TP and AP = AB + BP

becomes

AP = AT + TP and AP = TP + BP

AP = AT + TP and AP = BP + TP

So this means that

AP = AT + TP

BP + TP = AT + TP

BP + TP - TP = AT + TP - TP

BP = AT

AT = BP

which proves that segment AT is congruent to segment BP
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