The sum of the measures of the angles of a triangle is 180.
The proof of the Triangle Angle-Sum Theorem requires an auxiliary line. An auxiliary line is a line that you add to a diagram to help explain relationships in proofs. The red line in the diagram below is an auxiliary line.
Proof of Theorem 3-10: Triangle Angle-Sum Theorem
Given:
Prove:
Statements | Reasons |
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1) Draw
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1) Parallel Postulate |
2)
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2) that form a linear pair are suppl. |
3)
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3) Definition of suppl. |
4)
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4) Angle Addition Postulate |
5)
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5) Substitution Property |
6)
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6) If lines are ||, then alternate interior are
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7)
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7) Congruent have equal measure. |
8)
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8) Substitution Property |
When you know the measures of two angles of a triangle, you can use the Triangle Angle-Sum Theorem to find the measure of the third angle.