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2.5_Proofs_of_Angle_Theorems - Angle Theorems Paragraph...

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Angle Theorems
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Paragraph Proof
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Given: 1 & 2 are a linear pair Prove: 1 & 2 are supplementary 1 & 2 are a linear pair of angles formed by opposite rays BA and BC. Opposite rays form a straight angle so m ABC = 180°. By angle addition, m ABC = m 1 + m 2. Using substitution 180° = m 1 + m 2. Therefore by definition of supplementary angles, 1 & 2 are supplementary. 2 1 A B C
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If two angles form a linear pair, then they are supplementary.
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If two angles form a linear pair, then the sum of the angles is 180°.
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Given: 1 & 2 are a linear pair Prove: m 1 + m 2 = 180° 1. 1 & 2 are a linear pair 2. 1 + 2 are supplementary 3. m 1 + m 2 = 180° statements 1. Given 2. Linear pair supp. 3. supp. ’s sum 180° 2 1
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Supplements of the same angle or congruent angles are congruent.
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Given: A & B are supplementary C & B are supplementary Prove: A C 1. A & B are supp. C & B are supp. 2. m A + B = 180° m C + B = 180° 3. m A + m B = m C + m B statements 1. Given 2. If supp. ‘s sum = 180° 3. substitution B reasons
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