Lesson Plan #17. Class: Geometry Date: Thursday October 18 th, 2018
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1 Lesson Plan #17 1 Class: Geometry Date: Thursday October 18 th, 2018 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: Write the proof for the following ABD and ACE intersect Objectives: Students will be able to use definitions, postulates and theorems to prove statements. Note: Test #3 on Thursday October 26th 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 Theorem If two angles are congruent, their complements are congruent. Theorem If two angles are congruent their supplements are congruent Do Now: Recall the definition of a linear pair: A linear pair of angles are two adjacent angles whose sum is a straight angle. Fill in the missing reason in the proof <1 and <2 form a linear pair 1is supplementary to angle Given is a straight angle. 2. Definition of a linear pair 3. m 1 m <1 is supplementary to angle <2 4. Definition of supplementary angles 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? Theorem: If two angles form a linear pair, they are supplementary
2 Assignment #2: Fill in the missing reason in the proof 2 BEC and AED BEC AED are vertical angles B D E C A 1. BEC and AED are vertical angles Definition vertical angles. (1) 2. AEB and CED intersect at E. 3. AEC & BEC form a linear pair of angles. AED & AEC form a linear pair of angles 4. <BEC is the supplement of <AEC. 4. <AED is the supplement of <AEC. 5. <BEC <AED 5. Theorem If two angles are vertical angles, then they are congruent. 3. Definition of a linear pair of angles (2) Assignment #3: Complete the proof at the right. ect 1.CE bisects ADB 2. ADE BDE FDB and CDE intersect. 4. BDE and FDC are 4. vertical angles 5. BDE FDC Transitive Property of congruence (2,5) Assignment #4: Fill in the missing reasons
3 3 Assignment #5: Prove the following statement Sample Proof: 1. ABC 1. Given 2. r s 2. Given 3. m r m s 3. Definition of congruent angles (2) 4. BE bisects CBD 4. Given 5. BF bisects CBG 5. Given 6. m CBE m x m r 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 Same as reason 6 (1) 8. m CBE m x m r m CBF 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 x 13. Definition of an angle bisector (4) 14. m CBE m x 14. Definition of congruent angles (13) 15. CBF 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. x y 19. Definition of congruent angles (18)
4 Chapter Review: 4
5 Assignment #6: 5
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