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How would you do a two-column proof of the Corollary to the Triangle Sum Theorem: the acute angles of a right triangle are complementary, or m∠A + m∠B = 90°?
See below for the proof:
Statements (Reasons)
1) Right ##DeltaABC## with right ##/_C##. ( Given)
2) ##m/_A+m/_B+m/_C=180^@## (Triangle Sum Theorem)
3) ##m/_C=90^@## (Definition of a right angle)
4) ##m/_A+m/_B+90^@=180^@## (Substitution Property of Equality)
5) ##m/_A+m/_B=90^@## (Subtraction Property of Equality)
Note that in step 4, ##90^@## is substituted for ##m/_C## in the step 2 equation, since the two things are equal according to step 3.
Note that in step 5, ##90^@## is subtracted from both sides of the step 4 equation.