1. Over Lesson 2–5 5-Minute Check 1 In the figure shown, A, C, and lie in plane R, and B is on. Which option states the postulate that can be used to show that A, B, and C are collinear? Define: Algebraic Proof BellRinger

2. CCSS Content Standards Preparation for G.CO.9 Prove theorems about lines and angles. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others.

3. Then/Now You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties of equality to write geometric proofs.

4. Concept

5. Example 1 Justify Each Step When Solving an Equation Solve 2(5 – 3a) – 4(a + 7) = 92. Algebraic StepsProperties 2(5 – 3a) – 4(a + 7)=92Original equation 10 – 6a – 4a – 28=92Distributive Property –18 – 10a=92Substitution Property –18 – 10a + 18 =92 + 18Addition Property

6. Example 1 Justify Each Step When Solving an Equation Answer: a = –11 –10a=110Substitution Property Division Property a=–11Substitution Property

7. Example 1 A.a = 12 B.a = –37 C.a = –7 D.a = 7 Solve –3(a + 3) + 5(3 – a) = –50.

8. Example 2 Write an Algebraic Proof Begin by stating what is given and what you are to prove.

9. Example 2 Write an Algebraic Proof 2. d – 5 = 20t2. Addition Property of Equality StatementsReasons Proof: 1. Given 1. d = 20t + 5 4.4. Symmetric Property of Equality 3.3. Division Property of Equality = t

10. Example 2 Which of the following statements would complete the proof of this conjecture? If the formula for the area of a trapezoid is, then the height h of the trapezoid is given by.

11. Example 2 StatementsReasons Proof: 3.3. Division Property of Equality 4.4. Symmetric Property of Equality 1. Given 1. 2._____________2. Multiplication Property of Equality ?

12. Example 2 A.2A = (b 1 + b 2 )h B. C. D.

13. Groupwork: P139 #1-5 Homework: Worksheet 2-6

14. Example 3 Write a Geometric Proof If  A  B, m  B = 2m  C, and m  C = 45, then m  A = 90. Write a two-column proof to verify this conjecture.

15. Example 3 5. m  A = 90 5. Substitution StatementsReasons Proof: 4. Substitution 4. m  A = 2(45) Write a Geometric Proof 2. m  A = m  B 2. Definition of angles 1. Given 1.  A  B; m  B = 2m  C; m  C = 45 3. Transitive Property of Equality 3. m  A = 2m  C

16. Example 3

17. StatementsReasons Proof: 1. Given 1. 2.2. _______________ ? 3. AB = RS3. Definition of congruent segments 4. AB = 124. Given 5. RS = 125. Substitution

18. Example 3 A. Reflexive Property of Equality B. Symmetric Property of Equality C.Transitive Property of Equality D. Substitution Property of Equality

19. End of the Lesson