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1 Lesson Plan #17 Class: Geometry Date: Tuesday October 8th, 2013 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 7and 8 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 complementary 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 4 11. Definition of Congruent angles (10) 2 2 What theorem was just proven in the Do Now? 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 B Given: C E Prove: 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. Assignment #3: Complete the proof below Statements Reasons 3 Assignment #4: 4 Sample Proof: Statements 1. Reasons 1. Given 2. 2. Given 3. m< r= m<s 4. bisects 3. Definition of congruent angles (2) 4. Given 5. 5. Given bisects 6. Postulate – The sum of the degree measures of all the angles on one side of a given line whose common vertex is a given point on the line is 180 (1) 7. m<CBF + m<y + m<s = 180 7. Same as reason 6 (1) 8. m<CBE + m<x + m<r = m<CB F+ m<y + m<s 8. Transitive Property of Equality (6, 7) 9. m<r = m<s 9. Definition of congruent angles (2) 10. m<CBE + m<x + m<s = m<CBF + m<y + m<s 10. Substitution Postulate (8,9) 11. m<s = m<s 11. Reflexive Property of Equality 12. m<CBE + m<x = m<CBF + m<y 12. Subtraction Postulate (10,11) 13. <CBE is congruent to <x 13. Definition of an angle bisector (4) 14. m<CBE = m<x 14. Definition of congruent angles (13) 15. <CBF is congruent to <y 15. Definition of an angle bisector (5) 16. m<CBF = m<y 16. Definition of congruent angles 17. m<x + m<x = m<y + m<y 17. Substitution Postulate (12, 14, 16) Or 2m<x = 2m<y 18.m<x = m<y 18. Division Postulate (17) 19. 19. Definition of congruent angles (18) <x is congruent to <y 6. m<CBE + m<x + m<r = 180