 congruent complement and supplement theorems. Opener: Given:

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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

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.

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.

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, 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: 1 complementary to 2 3 complementary to 2 Proof: Since 1 Complementary to 2 and 3 Complementary to 2, 1 + 2 = 90 and 3 + 2 = 90 Then 2 = 90 - 1 and 2 = 90 - 3. Then 90 - 1 = 90 - 3 So 1 = 3 Therefore, 1 ≅ 3 Prove: 1 ≅ 3 1 2 3

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 1 Complementary to 2 and 3 Complementary to 4, Prove: 2 ≅ 4 1 + 2 = 90 and 3 + 4 = 90 A B C D 1 2 E F G H 3 4 Then 1 = 90 - 2 and 3 = 90 - 4. Since 1 ≅ 3 90 - 2 = 90 - 4 So 2 = 4 Therefore, 2 ≅ 4

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: 1 supplementary to 2 3 supplementary to 2 Proof: Since 1 supplementary to 2  and 3 supplementary to 2 Prove: 1 ≅ 3 A B C D E 1 2 3 1 + 2 = 180 and 3 + 2 = 180 Then 2 = 180 - 1 and 2 = 180 - 3 Thus 180 - 1 = 180 - 3 So 1 = 3 Therefore, 1 ≅ 3

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: 1 supplementary to 2 3 supplementary to 4 1≅ 3 Proof: Since 1 supplementary to 2  and 3 supplementary to 4 1 + 2 = 180 and 3 + 4 = 180 Then 1 = 180 - 2 and 3 = 180 - 4 Since 1≅ 3, 180 - 2 = 180 - 4 So 2 = 4 Therefore, 2 ≅ 4 2 1 3 4 A B C D E F G H Prove: 2 ≅ 4

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

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

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

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

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

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

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

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

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

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