1. 1Geometry Lesson: Angle Theorems (Day 1) Aim: Do Now: What are the theorems related to angles? (Day 1) O E A D C B Given: Prove: StatementReason 1) 2) 3) 4) 5) 6) 7) Given Def. Angle Bisector Addition Post. (1,3) Substitution Post. Def. Angle Bisector Partition Post.

2. 2Geometry Lesson: Angle Theorems (Day 1) Theorem #1: 1 2 Def. Right Angles Transitive Post. Def. congruent angles All right angles are congruent.

3. 3Geometry Lesson: Angle Theorems (Day 1) Def: A O C 1 2 Def: Complementary Angles are two angles whose measures add up to 90 degrees.

4. 4Geometry Lesson: Angle Theorems (Day 1) 70º 50º Ex: Complementary Angles 20º 1) A B 2) 40º B A x 3) A B 90-x 4)

5. 5Geometry Lesson: Angle Theorems (Day 1) Ex: Complementary Angles Proof A P B C D 1 2 3 Given: Prove: StatementReason 1) 2) 3) 4) 5) 6) 7) Given Def. comp. angles Substitution Postulate Reflexive Postulate Subtraction Postulate

6. 6Geometry Lesson: Angle Theorems (Day 1) Theorems #2, 3: 1 2 3 Theorem #2: Complements of the same angle, or congruent angles, are congruent. If the union of two adjacent angles is a right angle, the angles are complementary. Theorem #3: A CB D 1 2

7. 7Geometry Lesson: Angle Theorems (Day 1) Ex 1: Compl. Angles A P B C D 1 2 3 StatementReason 1) 2) 3) 4) 5) Given If the union of two adjacent angles is a right angle, the angles are compl. Given: Prove: Complements of the same angle, or congruent angles, are congruent. Def. perpendicular lines Partition Postulate

8. 8Geometry Lesson: Angle Theorems (Day 1) Ex 2,3,4: Compl. Angles: 1 2 3 4 ABCD P Q 2) Given: Prove: 3) Given: Prove: