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1 Lesson Plan #17 Class: Geometry Date: Wednesday October 10th, 2012 Topic: Using postulates and definitions to prove statements in geometry Aim: Students will be able to use postulates and definitions to prove statements in geometry? HW #17: Prove the conclusions in 7, 8 and 9 Objectives: Students will be able to use definitions, postulates and theorems to prove statements. Note: Below are the theorems we proved yesterday Theorem - If two angles are right angles, then they are congruent Theorem - If two angles are straight angles, then they are congruent Theorem - If two angles are complements of the same angle, then they are congruent Theorem - If two angles are supplements of the same angle, then they are congruent Do Now: Fill in the missing reason in the proof below Given: Prove: 3 Statements 1. 2. 4. 5. 6. 7. 8. 9. 10. 1 Reasons 1.Given 2.Given 3.Given 4. Definition of complimentary angles (3) 5. 6. Transitive property of equality (4,5) 7. 8. Substitution Postulate (6,7) 9. 10. or 11. PROCEDURE: Write the Aim and Do Now Get students working! Take attendance Give Back HW Collect HW Go over the Do Now What theorem was just proven in the Do Now? 11. Definition of Congruent angels (10) 4 2 2 A similar proof can be provided for the following theorem: If two angles are congruent, then their supplements are congruent. Recall the definition of a linear pair: A linear pair of angles are two adjacent angles whose sum is a straight angle. Assignment #1: Fill in the missing reason in the proof 1 2 Given: <1 and <2 form a linear pair Prove: Statements 1. 2. 3. 4. <1 is supplementary to angle <2 Reasons 1. Given 2. Definition of a linear pair 3. 4. Definition of supplementary angles Theorem: If two angles form a linear pair, they are supplementary Assignment #2: Fill in the missing reason in the proof Given: Prove: B C E D Statements 1. 2. and intersect at E 3. <BEC is the supplement of <AEC; <AED is the supplement of <AEC 4. <BEC <AED A Reasons 1. Given 2. Definition vertical angles 3. If two angles form a linear pair, they are supplementary 4. Theorem – If two angles are vertical angles, then they are congruent. Statements Reasons 3 Assignment #3: Complete the proof below