Morning Geometry! Pick up U1L12 from the side shelf.    Tonight’s HW: HW #17 Pg. 123 #5-6 Pg. 127 #1-9, 11 Finish writing notecards (they will be checked on Monday) 3rd due on 9/22 4th due on 9/22 Updates: Unit 1 Quiz 4 (2.6, 2.7) 3rd/4th will be 9/22

Agenda Review HW #16 Proof Practice! U1L12 Cool-Down… Students who need to take Assessments: 3rd Period – 4th Period – 1 min

HW #16 Pg. 113 #1-8 (8) a. Definition of right ∠ b. m∠1+m∠2 = m∠BAC (2) Theorem (4) a. Definition of Congruent Angles b. ∠1 and ∠2 are supplementary angles c. Substitution property of equality d. ∠1 and ∠3 are supplementary angles (6) 1. Given 2. Definition of ∠ Bisector 3. Definition of congruent ∠’s 4. Given 5. Substitution 6. ∠ Add. Postulate 7. Substitution 8. Simplify 9. Definition of right ∠ (8) a. Definition of right ∠ b. m∠1+m∠2 = m∠BAC c. m∠2 = m∠3 d. Substitution e. ∠1 and ∠3 are complementary

Proof Practice!

Proof Practice!

Proof Practice!

Proof Practice! Given: 1, 2 , 3, 4 Prove: m1 + m2 = m1 + m4 HINT: You will use a theorem we discussed at the end of our last class period.

Learning Objective By the end of this period you will be able to: Write two-column proofs as a paragraph proof.

Paragraph and Flow Chart Proofs (2.7) 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. 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!

Paragraph and Flow Chart Proofs (2.7) How to Write a Paragraph Proof Your first sentence should be the given information (hypothesis) Each sentence must include both the statement and the reason. The last sentence should be what you are trying to prove. (conclusion)

Paragraph and Flow Chart Proofs (2.7) Use the given template on your guided notes to write a sentence that involves all the statements and reasons of the following proof. Statements Reasons 1. 1 and 2 are right angles 1. Given 2. m1=90° m2 = 90° 2. Def of right angle 3. m 1 =m 2 3. Trans Prop of = 4. 1  2 4. Def of  angles

Paragraph and Flow Chart Proofs (2.7) 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. Therefore, by the definition of congruent angles, 1  2. NON-EXAMPLE Because 1 and 2 are right angles, they are congruent.

Paragraph and Flow Chart Proofs (2.7) See if you can write the paragraph proof for the above proof. (Yes, you must include complete sentences.)

Paragraph and Flow Chart Proofs (2.7) A proof that will come in handy for us and one that we already know, is the Vertical Angles Theorem. What do you remember about vertical angles?

Paragraph and Flow Chart Proofs (2.7) Proof of Vertical Angles Theorem:

Paragraph and Flow Chart Proofs (2.7) Proof of Vertical Angles Theorem:

Paragraph and Flow Chart Proofs (2.7) These next two proofs are very similar as to what you should expect on the Unit 1 Assessment! Let’s see if you can figure it out 

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.

Reflection – Answer the following questions independently. Cool-Down… Reflection – Answer the following questions independently. 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.

Prove-IT OR Hint-IT I am going to give you a blank proof and you and your tablemates are to work as hard as you can to figure out steps that make sense to you and your tablemates. Please write your final proof on one whiteboard. If you need a hint please raise your hand and I will write a step on a post-it note for you.

Prove-IT OR Hint-IT Given: m∠1+m∠3=180° Prove: ∠1 ≅ ∠4 Given: ∠1 ≅ ∠3 Prove: ∠2 ≅ ∠4