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fernandofhn1844
fernandofhn1844
13.03.2021 • 
Mathematics

Complete the proof that the sum of a triangle's interior angle measures is 180°180 \degree180°180, degree. StatementReason
1Construct DE↔\overleftrightarrow{DE}DE
D, E, with, \overleftrightarrow, on top through parallel to AC↔\overleftrightarrow{AC}AC
A, C, with, \overleftrightarrow, on top.Given a line, we can construct a parallel line through a point not on the given line.
2m∠A=m \angle A=m∠A=m, angle, A, equals
Alternate interior angles formed by parallel lines have equal measures.
3m∠B=65°m \angle B=65 \degreem∠B=65°m, angle, B, equals, 65, degreeGiven
4m∠C=m \angle C=m∠C=m, angle, C, equals
Alternate interior angles formed by parallel lines have equal measures.
5m∠A+m∠B+m∠C=180°m \angle A + m \angle B + m \angle C = 180 \degreem∠A+m∠B+m∠C=180°m, angle, A, plus, m, angle, B, plus, m, angle, C, equals, 180, degreeSubstitution and addition (2, 3, 4).
Did we prove the conclusion true for every triangle or only for this specific triangle?

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