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Writing Proofs

Writing Proofs. During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations. Recall: Properties of Equations. Addition: If a = b, then a + c = b + c , for all real numbers a, b, and c.

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Writing Proofs

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  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. Example1 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. Example2 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. Given.

  6. Example4 Write a complete proof of the following: Given: m ∠ x = 38; m ∠ y = 38 Prove: x y

  7. Example5 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. Example5

  9. Example6 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 = 21Prove: CD = 21 Diagram: A B C D

  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. Final Checks for Understanding

  13. Final Checks for Understanding

  14. Final Checks for Understanding

  15. Final Checks for Understanding

  16. HOMEWORK ASSIGNMENT Writing Simple Geometric Proofs WS

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