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One More Week Until Your Unit Test!!!

One More Week Until Your Unit Test!!!. Pick up notes from the front table Take out your homework from last night and a red pen . Take out your whiteboard and whiteboard marker. Start writing down the learning objective : SWBAT write paragraph proofs.

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One More Week Until Your Unit Test!!!

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  1. One More Week Until Your Unit Test!!! Pick up notes from the front table Take out your homework from last night and a red pen. Take out your whiteboard and whiteboard marker. Start writing down the learning objective: SWBAT write paragraph proofs. SWBAT write a two-column proof given a paragraph proof.

  2. Learning Objective • SWBAT write paragraph proofs. • SWBAT write a two-column proof given a paragraph proof.

  3. Math Joke of the Day • How is a geometry book like the United Nations? • They both have lots of rulers.

  4. Whiteboards! APK • Fill in the blanks: Given: 1 and 2 are right angles Prove: 1  2

  5. Whiteboards! APK Cont’d Given: 1 and 2 are right angles Prove: 1  2

  6. Essential Question for Today • How would you compare and contrast two-column and paragraph proofs?

  7. The Past Couple of Days… • We learned how to write a two-column proof! • Today, we are going to learn a second way of writing proofs, which are paragraph proofs. • Tomorrow, we are going to learn a third method which is a flow-chart proof.

  8. Paragraph Proofs • Just like writing paragraphs in English class, we are going to write proofs in complete sentences. • You still must include EVERY step and the reason behind each step. • To begin, let’s make each step in a two-column proof it’s own sentence!

  9. How to write a paragraph proof: • Your first sentence should be the given information ( home) • Each sentence must include both the statement and the reason. • The last sentence should be what you are trying to prove. (destination)

  10. Let’s recall what we just did with our whiteboards!: Right Angle Congruence Theorem Now Let’s Write a Paragraph Proof! Given: 1 and 2 are right angles Prove: 1  2

  11. Right Angle Congruence Theorem • Just like in a two-column proof, you always start with the given information. ( our home) • It is given that 1 and 2 are right angles • State the second step in a sentence By the definition of right angles, m1=90° and m2 = 90°

  12. Now, let’s write this in Paragraph form! • State the 3rd step By the transitive property of equality, m1 =m 2 • Remember, our last sentence should be what we are trying to prove. ( our destination) By the definition of congruent angles, 1  2

  13. Paragraph Proof of the Right Angle Congruence Theorem • EXAMPLE • It is given that 1 and 2 are right angles. By the definition of right angles, m1=90° and m2 = 90°. By the transitive property of equality, m1 =m 2. By the definition of congruent angles, 1  2. • NON-EXAMPLE • Because 1 and 2 are right angles,they are congruent.

  14. CFU • What should the first sentence be in a paragraph proof? • What should the last sentence be in a paragraph proof?

  15. Writing a Paragraph Proof with your Table Given: m1 + m2 = m4 Prove: m3 + m1 + m2 = 180°

  16. Think About • What should your first sentence be? • What should your last sentence be? • How many sentences should there be?

  17. Paragraph Proof It is given that m1 + m2 = m4. 3 and 4are supplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition of supplementary angles. By Substitution, m3 + m1 + m2 = 180°.

  18. Vertical Angle Theorem • From what you know about vertical angles, what do you predict the vertical angle theorem to say? • Think-pair-share

  19. Vertical Angle Theorem Vertical angles are congruent

  20. Now Let’s Write a Two-Column Prove Given a Paragraph Given: 1 and 3 are vertical angles Prove: 1  3

  21. Paragraph Proof:  1 and  3 are vertical angles. By the definition of vertical angles,  1 and  3 are formed by intersecting lines. Therefore,  1 and  2 are a linear pair and  2 and  3 are a linear pair by the definition of linear pairs. By the Linear Pair Theorem,  1 and  2 are supplementary, and  2 and  3 are supplementary. So by the Congruent Supplements Theorem,  1 is congruent to  3. • What do you think the first statement should be in your two column proof? Talk with your table! • How many steps do you think there are in this two-column proof?

  22. Fill this Two-Column Proof Out based on your Paragraph proof

  23. Challenge! • You just proved the Vertical Angles Theorem.  • Can you prove it another way? • First write it as a two-column proof • Then write it in paragraph form • Work with your table!

  24. Let’s Share!

  25. On a Separate Piece of Paper Write this Proof in Paragraph Form Given: 1  4 Prove: 2  3 Directions: First write this as a two-column proof individually. Then write this in paragraph form

  26. Whiteboards! How many sentences do you think there will be in this paragraph proof? Write the first sentence of this paragraph proof. Write the second sentence. Write the 3rd sentence. Write the 4th sentence.

  27. Closure • On the bottom of your notes, write down the similarities and differences of two-column proofs and paragraph proofs. • Which type do you prefer? Why? • What is your first sentence of a paragraph proof? If a two-column has 5 steps, how many sentences does the paragraph proof have? • Be ready to share out.

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