* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry Fall 2016 Lesson 017 _Using postulates and theorems to
Survey
Document related concepts
Algebraic K-theory wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Integer triangle wikipedia , lookup
History of geometry wikipedia , lookup
Noether's theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Four color theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
Transcript
1 Lesson Plan #17 Date: Friday October 21st, 2016 Class: Geometry 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 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 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 Given: <1 and <2 form a linear pair Prove: 1 is supplementary to angle 2 Statements 1. 1 and 2 form a linear pair 2. 1 2 is a straight angle. 3. m 1 m 2 180 4. <1 is supplementary to angle <2 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 Reasons 1. Given 2. Definition of a linear pair 3. 4. Definition of supplementary angles 1 2 Assignment #2: Fill in the missing reason in the proof B Given: C BEC and AED are vertical angles E Prove: D BEC AED A Statements Reasons 1. Given 2. Definition vertical angles. (1) BEC and AED are vertical angles 2. AEC and CED intersect at E. 3. AEC & BEC form a linear pair of angles. AED & AEC form a linear pair of angles 1. 3. Definition of a linear pair of angles (2) 3. <BEC is the supplement of <AEC. <AED is the supplement of <AEC. 4. <BEC <AED 3. 4. Theorem – If two angles are vertical angles, then they are congruent. Assignment #3: Complete the proof at the right. ect Assignment #4: Fill in the missing reasons Statements Reasons 1. CE bisects ADB 1. 2. ADE BDE 2. 3. FDB and 3. CDE intersect. 4. BDE and FDC are vertical angles 5. BDE FDC 4. 6. 6. Transitive Property of congruence (2,5) 5. 3 Assignment #5: Prove the following statement. Statements 1. Reasons 1. Sample Proof: Statements 1. ABC 2. r s 3. m r m s 4. BE bisects CBD 5. BF bisects CBG 6. m CBE m x m r 180 7. m CBF m y m s 180 8. m CBE m x m r m CBF m y m s 9. m r m s 10. m CBE m x m s m CBF m y m s 11. m s m s 12. m CBE m x m CBF m y 13. CBE x 14. m CBE m x 15. CBF y 16. m CBF m y 17. m x m x m y m y 2m x 2m y or 18. m x m y 19. x y Reasons 1. Given 2. Given 3. Definition of congruent angles (2) 4. Given 5. Given 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. Same as reason 6 (1) 8. Transitive Property of Equality (6, 7) 9. Definition of congruent angles (2) 10. Substitution Postulate (8,9) 11. Reflexive Property of Equality 12. Subtraction Postulate (10,11) 13. Definition of an angle bisector (4) 14. Definition of congruent angles (13) 15. Definition of an angle bisector (5) 16. Definition of congruent angles 17. Substitution Postulate (12, 14, 16) 18. Division Postulate (17) 19. Definition of congruent angles (18) 4 Chapter Review: 5 Assignment #6: