1. Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations

2. Recall: Properties of Equations Addition: If a = b, then a + c = b + c, for all real numbers a, b, and c. Subtraction: If a = b, then a - c = b - c, for all real numbers a, b, and c. Multiplication: If a = b, then a ∙ c = b ∙ c, for all real numbers a, b, and c. Division: If a = b, then a/c = b/c.

3. Example 1 What reason can you give for the following conclusion? If m ∠ AOB = m ∠ COD, then m ∠ AOB + m ∠ BOC = m ∠ BOC + m ∠ COD Addition Property of Equality ?

4. Example 2 What reason can you give for the following conclusion? If 2 (m ∠ P )= 80, then m ∠ P = 40. Division Property of Equality

5. Example 3 What conclusion can you draw based upon the given information? Give a reason for each statement. StatementReason 1. 2. 1. 2. Given.

6. Example 4 Write a complete proof of the following: Given: m ∠ x = 38; m ∠ y = 38 Prove: x  y StatementReason 1. 2. 3. 4. 1. 2. 3. 4.

7. Example 5 Give a reason for each step in the proof on the following slide. Given: m ∠ AOB + m ∠ BOC = m ∠ BOC + m ∠ COD Prove: ∠ AOB  ∠ COD

8. Example 5 StatementReason 1. 2. 3. 4. 1. 2. 3. 4.

9. Example 6 1. Draw and label a diagram based upon the given information. 2. Write the missing statements in the proof on the following slide. Directions:

10. Given: AB ≅ BC, BC ≅ CD, AB = 21 Prove: CD = 21 Diagram: A B C D STATEMENTREASON 1. AB ≅ BC1. 2. BC ≅ CD2. 3. _______3. 4. AB = CD4. 5. AB = 215. 6.

11. Final Checks for Understanding On the following slide, statements in the first column are given information. Use these to draw logical conclusion, then justify your reason for each corresponding conclusion.

12. StatementReason 1. XY = ZW and ZW = AB; AB = 9 2. 3. 1. AB = CD and AB = 8 2. 1.  XYZ   ABC and  ABC   RPG 2. 1. Given 2. 3. 1. Given 2. 1. 2. Final Checks for Understanding

13. StatementReason 1. m  ROA = m  POW ; m  POW = 78 2. 1. RT + LM = 19; LM = 12 2. RT + 12 = 19 1. Given 2. 1.Given 2.

14. Final Checks for Understanding StatementReason 1. m  SLC + m  RTU = 127; m  SLC = 18 2. 3. m  RTU = 109 1. AB = CD and AB = 8 2. 1. m  BIG = 83 2 (m  BIG) = 166 1.Given 2. 3. 1. Given 2. 1. 2.

15. Final Checks for Understanding StatementReason 1. m  1 + m  2 = m  2 + m  3 ; 2. m  2 = m  2 3. m  1 = m  3 1. HO + OT = OT + DG 2. OT= OT 3. HO = DG 1. Given 2. 3. 1. Given 2. 3.

16. HOMEWORK ASSIGNMENT Writing Simple Geometric Proofs WS