1. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
Opener:
Given:
If two of the non-straight angles 
are selected at random, find the 
probability that the angles are:
Answer
1. Supplementary
7/36
Answer
2. Complementary
1/9
Answer
3. Congruent
5/36

3. Advanced Geometry
Section 2.3 / 4 Drawing Conclusions / Congruent Supplements and  
 Complements
Learner Objective: Students will draw valid conclusions and will prove 
 angles congruent using congruent complement and supplement 
 theorems.

4. Procedure for Drawing Conclusions
Learner Objective: Students 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.

5. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.

7. If angles are complementary to the same angle,
Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
If angles are complementary to the same 
 angle,
then they are congruent.
Given: complementary to 2
3 complementary to 2
Proof: Since Complementary to 2
and 3 Complementary to 2,
= 90 and
= 90
Then =
and =
Then =
So = 3
Therefore, ≅ 3
Prove: ≅ 3 1 2 3

8. If angles are complementary to congruent angles,
Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
If angles are complementary to congruent 
 angles,
then they are congruent.
Given: 1 Complementary to 2
3 Complementary to 4
1 ≅ 3
Proof: Since Complementary to 2
and 3 Complementary to 4,
Prove: 2 ≅ 4
= 90 and
= 90 A B C D 1 2 E F G H 3 4
Then =
and =
Since ≅ 3 =
So = 4
Therefore, ≅ 4

9. If angles are supplementary to the same angle,
Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
If angles are supplementary to the same 
 angle,
then they are congruent.
Given: supplementary to 2
3 supplementary to 2
Proof: Since 1 supplementary to 2
 and 3 supplementary to 2
Prove: ≅ 3 A B C D E 1 2 3
= and
= 180
Then =
and =
Thus =
So = 3
Therefore, ≅ 3

10. If angles are supplementary to congruent angles,
Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
If angles are supplementary to congruent 
 angles,
then they are congruent.
Given: supplementary to 2
3 supplementary to 4
1≅ 3
Proof: Since supplementary to 2
 and supplementary to 4
= and
= 180
Then =
and =
Since 1≅ 3, =
So = 4
Therefore, ≅ 4 2 1 3 4 A B C D E F G H
Prove: ≅ 4

11. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.

12. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.

13. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.

14. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
Statement
Reason

15. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
Statement
Reason

16. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
Statement
Reason

17. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
Statement
Reason

18. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.
Assignment 2.4:
Pg. 79
#1-8, 10, 11

19. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.

20. Learner Objective: Students will draw valid conclusions and will prove angles congruent using
 congruent complement and supplement theorems.