Welcome Geometry! Please do the following: Pick up Math Station Worksheet and U1L7 from the side shelf. Homework: HW #10 Pg. 166 #1-9, 11, 16-21 Updates: 3rd period Unit 1 Quiz 2 is 9/4 (Thursday) 4th period Unit 1 Quiz 2 is 9/5 (Friday) Unit 1 Quiz 2 is 1.1-1.4, 3.1-3.2 3° Due – 9/4 4° Due – 9/5 2 mins

Agenda Math Stations U1L7 Cool-Down… 1 min

Math Stations You will be given 15 minutes to do as many problems as you can. Each station will contain two problems. Pick a station. When I say start you are to pick a station. Level 1-3 are basic, Level 4-6 are intermediate, and Level 7-9 are advanced. This is an independent exercise; therefore you are not to travel in groups. Complete the problems. When you feel you have the correct solutions go to the front whiteboard and choose the level you were working on. If you got the solutions correct you may move to another station. If you got the solutions incorrect you must correct your mistakes. If you cannot figure out your mistake you must raise your hand and I will assist you. The other students at the table may help you, but you cannot travel together nor share complete solutions. 1 min

Math Stations Consequences: If you are traveling in a pack I will ask you to separate. If there are too many students at a table I will ask specific people to choose a different table. If I see that you are copying another students work you will receive a ZERO on the activity. If you are telling a student the solution than you and the other student will receive a warning and then a ZERO on the activity. (You may help one another, but not share solutions.) 1 min

Math Stations Goals: For you and me to see what level you are at with the current curriculum. To challenge yourself. If you find level 3 is easy skip to level 7 and see what your mind can do. 1 min

Learning Objective By the end of this period you will be able to: Use the angles formed by a transversal to prove two lines are parallel.

Proving Lines Parallel (3.3) Before beginning 3.3 we must discuss the basics of postulates and theorems. Postulate A statement that is accepted as true without proof. Example: Theorem A statement that has been proven.

Proving Lines Parallel (3.3) Did you notice how both the sample postulate and theorem were written? Many postulates and theorems are written in a form called conditional statement or more informally, as an If then statement. Conditional Statement (If Then) Written in the form “if p, then q.” p is the hypothesis (similar to the subject in English) q is the conclusion (similar to the predicate in English)

Proving Lines Parallel (3.3) Conditional Statement (If Then) Written in the form “if p, then q.” p is the hypothesis (similar to the subject in English) q is the conclusion (similar to the predicate in English) As a table, discuss what the hypothesis and conclusion are. Hypothesis (If) – Two points line in a plane. Conclusion (Then) – The line containing those points lies in the plane.

Proving Lines Parallel (3.3) Above we see the theorem for corresponding angles. On your whiteboard see if you can write the theorem for same-side interior angles. Identify the hypothesis and conclusion. On the other side of the whiteboard write the same theorem you just created but now switched. If q, then p; switch the hypothesis and conclusion.

Proving Lines Parallel (3.3) Converse A statement formed by switching the hypothesis and conclusion. If q, then p. Last week we found that IF a transversal cut two parallel lines, THEN alternate interior/exterior and corresponding angles were congruent and same-side interior angles were supplementary. This week we are looking at the converse; IF two lines are cut by a transversal such that a pair of alternate exterior angles are congruent, THEN ________________________. the two lines are parallel.

Proving Lines Parallel (3.3) Converse of the Alternate Exterior Angles Theorem If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel. For the next 5 minutes, you are expected to complete the converse theorem for alternate interior, corresponding, and same-side interior angles. Converse of the Alternate Interior Angles Theorem If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.

Proving Lines Parallel (3.3) Converse of the Corresponding Angles Theorem If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel. Converse of the Same-Side Interior Angles Theorem If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.

Proving Lines Parallel (3.3) We will do (a) together and then you will be expected to complete (b) and (c) with your tablemates.

Whiteboards! Use the given information and the theorems you have learned to show that r || s. m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5

Proving Lines Parallel (3.3) Attempt practice (2) and (3) in your tables. See what you can do!

Proving Lines Parallel (3.3) Attempt practice (2) and (3) in your tables. See what you can do!

Cool-Down… 3-2-1 Processing: List 3 main ideas from todays lesson. List 2 interesting points. List 1 question.

Pictionary With Math! You are going to be on two teams. Left of the room vs. the right of the room. I will choose 5 people at random. Choose the names and stand in two lines at the front of the room. I will show the first person in line a vocab word and they are to think of words that describe it [If you say the vocab word you loose that point automatically]. Everyone in their team are to guess that word and when that word is said the first person in line will place their card on the table and move to the back of the line and the next person will describe the next vocab word. If you cannot describe the word you may say pass and it will go to the person next in line. After the minute we will count the number of cards you won. Then the next team will go. Whoever is able to define the most words will win.

Notecards For the remainder of the period I expect you to begin writing notecards. On these notecards you should be writing information that you do not want to forget. For example, I would write Converse on one side and my own definition of converse on the other side. You may draw pictures or examples; these are your cards hence they must be helpful to you!