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Advanced Geometry
Unit 2 Basic Concepts and Proofs
2-2.3 / 4 Drawing Conclusions / Congruent Supplements and Complements
OBJECTIVE: I will will draw valid conclusions and will prove angles congruent using congruent
complement and supplement theorems.
Procedure for Drawing Conclusions
1. Memorize theorems, definitions, and postulates.
2. Look for key words and symbols in the given information.
3. Think of all the theorems, definitions, and postulates that involve those keys.
4. Decide which theorem, definition, or postulate allows you to draw a conclusion.
5. Draw a conclusion, and give a reason to justify the conclusion. Be certain that you have
not used the reverse of the correct reason.
Given:
 1 complementary to  2
 3 complementary to  2
Conclusion:
This leads us directly into the following theorem…
Theorem (Congruent Complement Theorem)
If two angles are _________________________________
then _____________________________________
PROOF:
Given:
 1 complementary to  2
Prove:
 1   3
 3 complementary to  2
Theorem (Congruent Complements Theorem)
If two angles are _________________________________
then _____________________________________
PROOF:
Given:
 1 complementary to  2
Prove:
 1   3
 2  4
 3 complementary to  4
Theorem (Congruent Supplement Theorem)
If two angles are _________________________________
then _____________________________________
PROOF:
Given:
 1 supplementary to  2
Prove:
 3 supplementary to  2
 1   3
Theorem (Congruent Supplements Theorem)
If two angles are _________________________________
then _____________________________________
PROOF:
Given:
Prove:
 1 supplementary to  2
 3 supplementary to  4
 1   3
2  4