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Theorem 2-7 If two angles are supplements of congruent angles (or of the same angle),  then the two angles are congruent.
Given:  1 and   2 are supplementary;  3 and   4 are supplementary  2      4 Prove:  1      3 Statements Reasons 1.    1 and   2 are supplementary;  3 and   4 are supplementary 1.  Given 2.   m  1 +  m  2 = 180; m  3 +  m  4 = 180 2.  Definition of supplementary angles 3.   m  1 +  m  2 = m  3 +  m  4  3.  Substitution 4.    2      4, or  m  2 =  m  4  4. Given, Definition of     5.   m  1 =  m  3, or   1      3  5. Subtraction Prop of =, Definition of   1 2 3 4
Theorem 2-8 If two angles are complements of congruent angles (or of the same angle),  then the two angles are congruent.
 
 
Practice Assignment Page 63 1-18

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GH 2-6

  • 1.
  • 2. Read page 61 – the top 4 paragraphs Suggestions:
  • 3. Theorem 2-7 If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.
  • 4. Given:  1 and  2 are supplementary;  3 and  4 are supplementary  2   4 Prove:  1   3 Statements Reasons 1.  1 and  2 are supplementary;  3 and  4 are supplementary 1. Given 2. m  1 + m  2 = 180; m  3 + m  4 = 180 2. Definition of supplementary angles 3. m  1 + m  2 = m  3 + m  4 3. Substitution 4.  2   4, or m  2 = m  4 4. Given, Definition of  5. m  1 = m  3, or  1   3 5. Subtraction Prop of =, Definition of  1 2 3 4
  • 5. Theorem 2-8 If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.
  • 6.  
  • 7.