One More Week Until Your Unit Test!!! Pick up the notes from the front table.    Tonight’s HW: HW Pg. 123 #5-6 Pg. 127 #1-9, 11 Bring a pack of notecards by Monday! Updates: No quiz on Monday Thursday/Friday: Unit 1 TEST

Agenda Review HW Challenge question in section 1.2 Review quiz Proof Practice! Paragraph Proofs Cool-Down… 1 min

HW 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

Take out your 1. 2: Measuring Segments notes Take out your 1.2: Measuring Segments notes. Work on the challenge problem! M, N, O, P, and Q are on line s such that N is the midpoint of MQ, O is the midpoint of NQ, and P is the midpoint of OQ. If MP = 8, then what is MQ? I expect 100% of you to work on this. If you do not have your notes, use a separate piece of paper and transfer the notes over!

Quiz #4 A: 11.5-13 B: 10.5-11 C: 9- 10 Below a 9, please come see me during tutorial! Students who still need to take the assessment: Period 1: Colin Period 6:Audrinna

Quiz #4

Geometric Proof (2.6) This proof is very similar to Practice (2b). See if you and your tablemates can come up with this complete proof without my help. Good Luck!

Proof Practice!

Proof Practice! Hint: Separate the givens into two steps

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 Write paragraph proofs.

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. On Monday, we are going to learn a third method which is a flow-chart proof.

Paragraph and Flow Chart Proofs (2.7) 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)

Whiteboards! Given: 1 and 2 are right angles Prove: 1  2 Statements Reasons 1. 1. Given 2. m1=90° m2 = 90° 2. . 3. . 3. Trans Prop of = 4. 1  2 4. 2. Def of right angle 3. 1=2 4. Def of congruent angles

Whiteboards! Given: 1 and 2 are right angles Prove: 1  2 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) 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

Right Angle Congruence Theorem Just like in a two-column proof, you always start with the given information. ( our hypothesis) 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°

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 conclusion) By the definition of congruent angles, 1  2

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.

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

Practice 2a See if you can write the paragraph proof for the above proof. (Yes, you must include complete sentences.)

Writing a Paragraph Proof with your Table Given: m1 + m2 = m4 Prove: m3 + m1 + m2 = 180° Have students put their paragraph proo under the document camera Simiarities/ differences Critique the examples

Paragraph Proof It is given that m1 + m2 = m4. 3 and 4 are 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°.

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

Paragraph and Flow Chart Proofs (2.7)

Paragraph and Flow Chart Proofs (2.7) Proof of Vertical Angles Theorem: Sometimes it is easier to write it as two columns first. My hint is that there are 5 steps.

Paragraph and Flow Chart Proofs (2.7) Proof of Vertical Angles Theorem: If there are 5 steps, how many sentences do you think you will need?

Paragraph and Flow Chart Proofs (2.7) Proof of Vertical Angles Theorem: Now write this is in paragraph form!!

Remember: Theorems you have to PROVE! Postulates you have to accept as TRUTH! In the next example you are proving Alternate Interior Angles and the Converse of that! You cannot use that in your proof since you are trying to prove it. Note: Corresponding Angles was a POSTULATE; therefore you can use it in your proof!

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