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3-3 Proving Lines Parallel What you need……. PHONES AWAY New Warm-Up Sheet Pencil/Pen Notebook Holt McDougal Geometry 3-3 Proving Lines Parallel Warm-Up 10/24 1. Go grab your assigned chrome book 2. Go to my website 3. Scroll to bottom and click link for Student Feedback Survey 4. Take your time to think and complete this survey. BE HONEST. THIS IS NOT FOR A GRADE. 5. When finished, go to Khan Academy and complete Line and Angles module and One-step inequalities module Holt McDougal Geometry 3-3 Proving Lines Parallel What you need……. TURN PACKET IN! PHONES AWAY New Warm-Up Sheet Pencil/Pen Notebook Holt McDougal Geometry 3-3 Proving Lines Parallel Warm-Up 10/25 If l ll m, find the value of each missing variable(s). Holt McDougal Geometry 3-3 Proving Lines Parallel Objective I can use what I know about angles formed by a transversal to prove two lines are parallel. PROVE IT?! Holt McDougal Geometry 3-3 Proving Lines Parallel What is the difference between these two statements? Hypothesis: "If the space shuttle was launched, then a cloud of smoke was seen." Converse: "If a cloud of smoke was seen, then the space shuttle was launched The Converse of a theorem is found by switching the hypothesis and conclusion. Holt McDougal Geometry 3-3 Proving Lines Parallel Holt McDougal Geometry 3-3 Proving Lines Parallel Check It Out! Example 1a Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m 1 = m 3 1 3 ℓ || m Holt McDougal Geometry 1 and 3 are corresponding angles. Conv. of Corr. s Post. 3-3 Proving Lines Parallel Holt McDougal Geometry 3-3 Proving Lines Parallel Holt McDougal Geometry 3-3 Proving Lines Parallel What you need…….TURN PACKET IN THAT WAS DUE YESTERDAY PHONES AWAY Warm-Up Sheet Pencil/Pen Proving Lines Parallel Sheet from yesterday Holt McDougal Geometry 3-3 Proving Lines Parallel Warm-Up 10/26 Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. Given:4 8 4 8 ℓ || m Holt McDougal Geometry 4 and 8 are corresponding angles. Conv. of Corr. s Post. 3-3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r , 1 3 Prove: ℓ || m Holt McDougal Geometry 3-3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r 1. Given 2. 1 3 2. Given 3. 3 2 3. Alt. Ext. ’s Thm. 4. 1 2 4. Trans. Prop. of 5. ℓ ||m 5. Conv. of Corr. s Post. Holt McDougal Geometry 3-3 Proving Lines Parallel You have 6 minutes to work on #3 and #4 from our worksheet yesterday. #4 is challenging but I BELIEVE IN YOU! Holt McDougal Geometry 3-3 Proving Lines Parallel Example 1B: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30 m3 = 4(30) – 80 = 40 m7 = 3(30) – 50 = 40 Substitute 30 for x. Substitute 30 for x. m3 = m7 3 7 ℓ || m Trans. Prop. of Equality Def. of s. Conv. of Corr. s Post. Holt McDougal Geometry 3-3 Proving Lines Parallel For the next part of class, you need a white board, marker and eraser. EVERYONE NEEDS ONE OF EACH. Holt McDougal Geometry 3-3 Proving Lines Parallel Example 2B Continued Use the given information and the theorems you have learned to show that r || s. m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5 m2 + m3 = 58° + 122° = 180° r || s Holt McDougal Geometry 2 and 3 are same-side interior angles. Conv. of Same-Side Int. s Thm. 3-3 Proving Lines Parallel Check It Out! Example 2b Refer to the diagram. Use the given information and the theorems you have learned to show that r || s. m3 = 2x, m7 = (x + 50), x = 50 m3 = 2x = 2(50) = 100° Substitute 50 for x. m7 = x + 50 = 50 + 50 = 100° Substitute 5 for x. m3 = 100 and m7 = 100 3 7 r||s Conv. of the Alt. Int. s Thm. Holt McDougal Geometry 3-3 Proving Lines Parallel What you need…….TURN PACKET IN AND TURN IN PROVING LINES PARALLEL WS!! PHONES AWAY Warm-Up Sheet Pencil/Pen Notes Holt McDougal Geometry 3-3 Proving Lines Parallel Warm-Up 10/27 Refer to the diagram to the right. Use the given information and the theorems you have learned to show that n ll p Holt McDougal Geometry 3-3 Proving Lines Parallel Example 4: Carpentry Application A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel. Holt McDougal Geometry 3-3 Proving Lines Parallel Check It Out! Example 4 What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where y = 8. Show that the oars are parallel. 4y – 2 = 4(8) – 2 = 30° 3y + 6 = 3(8) + 6 = 30° The angles are congruent, so the oars are || by the Conv. of the Corr. s Post. Holt McDougal Geometry