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Understanding Congruent Supplements and Complements Theorems in Geometry

This lesson covers Theorems 4 to 7 regarding congruent angles that are supplementary and complementary to other angles. Theorems state that if angles are supplementary to the same angle, or to congruent angles, they are congruent themselves. The lesson emphasizes understanding with picture examples and requires students to recognize the need for specific statements related to supplementary and congruent angles. Students will also review proofs from the textbook and complete related homework exercises on page 79.

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Understanding Congruent Supplements and Complements Theorems in Geometry

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  1. 2.4 Congruent Supplements and Compliments

  2. Theorem 4 If angles are supplementary to the same angle, then they are congruent Picture example: Must state: supplementary (twice, using one angle twice)

  3. Theorem 5 If angles are supplementary to congruent angles, then they are congruent. Picture Example: Must state: supplementary (twice) and congruency

  4. Theorem 6 If angles are complementary to the same angle, then they are congruent Picture Example: Must state: Complementary (twice, using the one angle twice)

  5. Theorem 7 If angles are complementary to congruent angles, then they are congruent Picture Example: Must State: supplementary (twice) and congruency

  6. Proofs page 77-78 With yourself or the person next to you, go over the four example proofs in the book Notice that the proofs are much longer than we have done before Notice what needs to be stated to use any of the theorems from today Sometimes you will also have to supply the conclusion.

  7. Homework Pg. 79 # 1-8, 12-15 Number 7 has 6 steps

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