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proofs involving parallel and perpendicular lines

To use this website, please enable javascript in your browser. Equations of parallel and perpendicular lines 7. Parallel and Perpendicular Lines Proofs. Same-side exterior angles: Angles 1 and 7 (and 2 and 8) are called same-side exterior angles — they’re on the same side of the transversal, and they’re outside the parallel lines. The product of perpendicular slopes is -1. If E is on AC , then E lies in plane P. 7. • Lines p and q are both perpendicular to s, so by the Lines Perpendicular to a Transversal Theorem, p is parallel to q. Click, We have moved all content for this concept to. Table of Contents Day 1 : SWBAT: Apply the properties of equality and congruence to write algebraic proofs Pages 1- 6 HW: page 7 Day 2: SWBAT: Apply the Addition and Subtraction Postulates to write geometric proofs Pages 8-13 HW: pages 14-15 Day 3: SWBAT: Apply definitions and theorems to write geometric proofs. According to result 2, if two sides of two adjacent acute angles are perpendicular, then the angles are complementary. 4. MEMORY METER. Back to Course Index. 5x–2y–9 = 0 and ay+2x–11 = 0. are perpendicular to each other. The lines can be parallel, perpendicular, or neither. LINES & ANLGES-Proofs involving parallel lines (part 2) LINES & ANGLES- Measuring an angle with the protractor. To use this website, please enable javascript in your browser. If plane P and plane Q intersect, then they intersect in a line. Bell Work: Write the three theorems on page 150 into your notes ... •Perpendicular Transversal Theorem –In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. Practice. Preview; MEMORY METER. Geometry. This geometry video tutorial explains how to prove parallel lines using two column proofs. Unit 2 Notes ­ Parallel, Perpendicular and Proofs OH MY.notebook 5 September 27, 2019 Aug 22­9:10 PM If two parallel lines are cut by a transversal, then a.alternate interior angles are ≅. MEMORY METER. 3.1 Conditional Statements. Perpendicular lines are intersecting lines. 3. If E is on AC , then E lies in plane P. 7. Once students have parallel lines proofs down, we move to writing equations of parallel and perpendicular lines. 5. Angle bisectors. Click, MAT.GEO.205.04 (Proofs involving Parallel and Perpendicular Lines - Geometry). You can sum up the above definitions and theorems with the following simple, concise idea. So, it's always new information in Geometry and then a quick review in Algebra 2. The given lines are written in y = mx + b form, with m = −8 for the first line and m = for the second line.. Identify the slopes of the given lines. 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). A is not in plane Q, then A is not on BD . 2. Slopes of Parallel Lines (or segments) Recall two lines are parallel if they do not ever intersect. 8. Click, We have moved all content for this concept to. You have just tried describing parallel and perpendicular lines… 1. Solving Real-Life Problems • This photo shows the layout of a neighborhood. Parallel and Perpendicular Lines 143 Conditional Statements Identify the hypothesis and conclusion of each conditional. You are viewing an older version of this Read. A is not in plane Q, then A is not on BD . If plane P and plane Q intersect, then they intersect in a line. Lines that do not intersect are parallel lines. At both of the schools where I've taught, my students haven't learned equations of parallel and perpendicular lines in Algebra 1. Memo line for the parallel and perpendicular lines worksheet. Plot the right triangle with vertices: and Find the slope of AB. Proofs involving parallel lines II Checkpoint: Definitions of geometric objects E. Lines in the coordinate plane. If 6. Click, Proofs involving Parallel and Perpendicular Lines, MAT.GEO.205.04 (Proofs involving Parallel and Perpendicular Lines - Geometry). note: moving each point the same distance and direction will produce a parallel line (and a coresponding angle) Proof of parallel lines/alt. This indicates how strong in your memory this concept is. Problem 1. Definition of Congruence: Having the exact same size and shape and there by having the exact same measures. This page will be removed in future. Start studying HCHS Geometry Unit 1B C2-C3 Proofs involving Angles and Parallel Lines. % Progress . 4. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Section 3.4 – Parallel and Perpendicular Lines. Showing top 8 worksheets in the category - Parallel Lines Proofs. We have a new and improved read on this topic. Begin with one sheet of 81 ” by 11” paper. ... Perpendicular Lines. Determine if AB is parallel to CD. PAP Geometry: Unit 3 – Proofs Involving Parallel and Perpendicular Lines 3.6 Practice – Proofs Involving Parallel and Perpendicular Lines No Textbook Correlation . y/2 = x–p and ax+5 = 3y. Practice this topic. A carpenter plans to install molding on the sides and the top of the doorway. m, rn2 In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is Negative reciprocals Find an equation of the line parallel to y = - -x + 2 passing through (8, -3). When lines and planes are perpendicular and parallel, they have some interesting properties. Preview; You will investigate the concept of proof and discover the importance of proof in mathematics. Example. −8 ≠ , so the lines are not parallel. This indicates how strong in your memory this concept is. I can do so many different activities. 2. This indicates how strong in your memory this concept is. 1. COORDINATE GEOMETRY-Slopes of parallel and perpendicular lines: Problem type 2. We have a new and improved read on this topic. Proofs involving lines with slopes that are equal or opposite reciprocals of each other. Preview; To determine if line segments are parallel, calculate their slopes. Name _____ Date _____ Period _____ Choose the word(s) that best completes the statements. Divide both sides by 3. x = 31. b.alternate exterior angles are ≅. 1. Problem. Parallel and perpendicular line segments. I lines = slopes … Do better in math today Get Started Now. Graph a linear equation 4. 3x - 3 = 90. The perpendicular transversal theorem states that if there are two parallel lines in the same plane and there's a line perpendicular to one of them, then it's also perpendicular to the other one. Parallel and 3 Perpendicular Lines 3.1 Identify Pairs of Lines and Angles 3.2 Use Parallel Lines and Transversals 3.3 Prove Lines are Parallel 3.4 Find and Use Slopes of Lines 3.5 Write and Graph Equations of Lines 3.6 Prove Theorems About Perpendicular Lines In previous chapters, you learned the following skills, which you’ll use in Prove theorems about perpendicular lines. Theorem 10.1: Given a point A on a line l, there exists a unique line m perpendicular to l which passes through A.; The drawing is shown in Figure 10.2. If 6. c. corresponding angles are ≅. ... plane review 2. Write the converse of each conditional statement. Determine whether the lines y = − 8x + 5 and are parallel, perpendicular, or neither.. 8. Definition of Angle Bisector: The ray that divides an angle into two congruent angles. Once students have parallel lines proofs down, we move to writing equations of parallel and perpendicular lines. MEMORY METER. Parallel and Perpendicular Lines 143 Conditional Statements Identify the hypothesis and conclusion of each conditional. 4. interior angles: IV. The slopes Of perpendicular lines are negative reciprocals. Proof . Skew lines are coplanar. Determine whether the converse is true. Prove theorems about perpendicular lines. Perpendicular Lines Theorems. Slopes of lines 3. % Progress . 3.3 Prove Lines are Parallel FCA 5 #1-11 Hw: Proving Lines Parallel Worksheet Extra Practice 3.3 Proving Lines Parallel 3.3 Prove Lines are Parallel FCA 6 ALL Hw: p 151 # 41* (use paragraph form), pp 160 - 161 # 31*, 36, 37 **You will be turning in # 41, 31** FCA 3.3 Prove Lines are Parallel ALL 7 … Practice. 2. Create. Problems Worksheet. a. are parallel, then find a. Skew lines are coplanar. The carpenter cuts the ends of the top piece and one end of each of the sides pieces 45 degrees as shown. Proofs involving lines with slopes that are equal or opposite reciprocals of each other. Proving Lines Are ParallelGeometryProving Relationships Between LinesProofs Involving Perpendicular LinesLet's Get ParallelProofs About Alternate AnglesParallel Lines and Supplementary AnglesUsing Parallelism to Prove PerpendicularityProving Lines Are Parallel When you were given Postulate 10. 3. Proofs involving lines with slopes that are equal or opposite reciprocals of each other. The opposite reciprocal of −8 is , so the lines are perpendicular. 2 Parallel Perpendicular Reading and Writing As you read and study the chapter, write examples and notes about parallel and perpendicular lines on index cards. This indicates how strong in your memory this concept is. If two lines are parallel to a third line, then the two lines are parallel. Parallel lines have equal slopes. WORD PROBLEMS INVOLVING PARALLEL AND PERPENDICULAR LINES WORKSHEET. • Also, lines s and t are both perpendicular to q, so by the Lines Perpendicular to Honors Geometry Chapter 3 Proofs Involving Parallel and Perpendicular Lines Practice Proofs Involving Showing top 8 worksheets in the category - Proofs Of Parallel And Perpendicular Lines. Eg.l. Write and apply proofs about parallel and perpendicular lines. Problem 4 : In the diagram given below, the lines m and n are perpendicular. Write and apply proofs about parallel and perpendicular lines. Proving Lines Are ParallelGeometryProving Relationships Between LinesProofs Involving Perpendicular LinesLet's Get ParallelProofs About Alternate AnglesParallel Lines and Supplementary AnglesUsing Parallelism to Prove PerpendicularityProving Lines Are Parallel … Add 3 to both sides. Transversal is a line that intersects two or more lines. 3. geometric proofs vocabulary for Parallel lines Learn with flashcards, games, and more — for free. Equations of lines 5. Sec 2.6 Geometry – Triangle Proofs Name: COMMON POTENTIAL REASONS FOR PROOFS . You can use some of these properties in 3-D proofs that involve 2-D concepts, such as proving that you have a particular quadrilateral or proving that two triangles are similar. Parallel and Perpendicular Lines Proofs. Solve real-life problems involving perpendicular lines. Honors Geometry Chapter 3 – Proofs Involving Parallel and Perpendicular Lines Practice – Proofs Involving Parallel and Perpendicular Lines No Textbook Correlation Name _____ Date _____ Period _____ Choose the word(s) that best completes the statements. Oops, looks like cookies are disabled on your browser. PERPENDICULAR AND PARALLEL – Angles, parallel lines and transversals Search. Construct perpendicular lines. 3.2 Deductive Reasoning. So, we have (x+3) ° + (2x-6) ° = 90 ° x + 3 + 2x - 6 = 90 Simplify. Pages 16-24 HW: pages 25-27 Day 4: SWBAT: Apply theorems about Perpendicular Lines 1. 1. Parallel and Perpendicular LinesMake this Foldable to help you organize your notes. Proofs Involving Parallel Lines Worksheet Answers / Ixl Proofs Involving Triangles I Geometry Practice / M 2 m 3 1800 substitution prop.. This indicates how strong in your memory this concept is, Slope of Parallel and Perpendicular Lines. 6. Aug 18, 2016 - In this READY TO GO digital activity, students will use moveable pieces to write proofs about parallel and perpendicular lines. Proofs Parallel Lines - Displaying top 8 worksheets found for this concept.. Structure Worksheet. Don't just watch, practice makes perfect. Parallel and Perpendicular Lines Worksheet Answers. Unit 3 - Proof and Reasoning. non-vertical lines are parallel if and only if they have the same slope. 1. Slopes of parallel and perpendicular lines 6. You will extend your knowledge of the characteristics of angles and parallel and perpendicular lines and explore practical applications involving angles and lines. View proofs_parallel_perp_lines_key.pdf from MATH 102 at California State University, Fullerton. Three parallel planes: If two planes are parallel to the same plane, […] Question 1 : If the straight lines. LINES & ANGLES-Drawing an angle with the protractor. 5. Construct perpendicular lines. Parallel Line Postulate: If 2 parallel lines are cut by a transversal, then their coresponding angles are congruent. View proofs_parallel_perp_lines.pdf from SCIENCE SC003 at Marquette High School. It is kind of like using tools and supplies that you already have in order make new tools that can do other jobs. To better organize out content, we have unpublished this concept. Definition of Midpoint: The point that divides a segment into two congruent segments. 3.4 Angle Pairs. ... plane review 2. Given a line l and a point A on l, suppose there are two lines, m and n, which both pass through A and are perpendicular to l. % Progress . Honors Geometry Chapter 3 – Proofs Involving Parallel and Perpendicular Lines Practice – Proofs Involving Parallel and Perpendicular Lines No Textbook Correlation Name _____ Date _____ Period _____ Choose the word(s) that best completes the statements. Determine which lines, if any, must be parallel in the diagram. SWBAT: Write proofs involving Parallel and Perpendicular lines Warm Up (Page 10) 40° 60° 30° 30° x = 60° + 30 ° = 90 ° Slopes of lines 3. Browse. Parallel Lines and Transversals Worksheet Answers. Proofs with Perpendicular lines Learning Target I can describe, draw and write a two column proof involving angle relationships of perpendicular lines cut by a transversal. View proofs_parallel_perp_lines.pdf from SCIENCE SC003 at Marquette High School. Perpendicular bisectors. Section 3.3 Proofs with Parallel Lines 137 3.3 Proofs with Parallel Lines Exploring Converses Work with a partner. PERPENDICULAR AND PARALLEL – Angles, parallel lines and transversals Search. Justify your conclusion. 3.3 Introduction to Proof. Students will LOVE practicing proofs with this digital activity. Parallel lines proofs worksheet honors geometry mr. We are going to use them to make some new theorems, or new tools for geometry. When we're dealing with a pair of lines, three relationships are possible. Oops, looks like cookies are disabled on your browser. % Progress . When lines are parallel, they will never intersect (touch/cross) because they have the same slope, and are therefore always the … 3x = 93. 8. Equations of lines 5. Honors Geometry Chapter 3 Proofs Involving Parallel and Perpendicular Lines Practice - Proofs Involving Parallel and Angles and Lines Topics: 1. At both of the schools where I've taught, my students haven't learned equations of parallel and perpendicular lines in Algebra 1. Equations of parallel and perpendicular lines 7. A simple sketch can show the parallel line postulate. LINES & ANGLES-Acute, obtuse, and right angles. The old tools are theorems that you already know are true, and the supplies are like postulates. This page will be removed in future. 148 Chapter 3 Parallel and Perpendicular Lines 3.4 Lesson WWhat You Will Learnhat You Will Learn Find the distance from a point to a line. Practice. Lines that do not intersect are parallel lines. Draw line c perpendicular to line b This indicates how strong in your memory this concept is, Slope of Parallel and Perpendicular Lines. Any two vertical lines are parallel. Preview; The Results for Parallel Lines Proofs Worksheet Answers. Unit 1 Lesson 13 Proving Theorems involving parallel and perp lines WITH ANSWERS!.notebook 3 October 04, 2017 Oct 3­1:08 PM note: You may not use the … So, it's always new information in Geometry and then a quick review in Algebra 2. 3.7 Proofs Involving Parallel and Perpendicular Lines 1. You have just tried describing parallel and perpendicular lines… Slopes of parallel and perpendicular lines 6. Proofs Of Parallel And Perpendicular Lines - Displaying top 8 worksheets found for this concept.. 3.4b Congruent Complements and Supplements - not covered in 2013. Solve real-life problems involving perpendicular lines. Aug 18, 2016 - In this READY TO GO digital activity, students will use moveable pieces to write proofs about parallel and perpendicular lines. Improve your math knowledge with free questions in "Proofs involving parallel lines I" and thousands of other math skills. Students will LOVE practicing proofs with this digital activity. 4. You are viewing an older version of this Read. Parallel line proofs. Perpendicular lines are intersecting lines. We know that if we have two lines that are parallel-- so let me draw those two parallel lines, l and m. So that's line l and line m. We know that if they are parallel, then if we were to draw a transversal that intersects both of them, that the corresponding angles are equal. Perpendicular line proofs. In this lesson we will focus on some theorems abo… Proofs involving Parallel and Perpendicular Lines. 3.4 Proofs with Perpendicular Lines VOCABULARY LEARNING TARGETS • I can find the distance from a point to a line • I can construct perpendicular lines • I can prove theorems about perpendicular lines • I can solve real-life problems involving two lines that intersect at a right angle. Practice. Problems Worksheet. Chapter 3 : Parallel and Perpendicular Lines Day Activity & Assignment Notes ... 3.3 Prove Lines are Parallel ALL 7 Extra Proof Practice Hw: pp 159 - 160 # 34, 35 (use paragraph form), 40 - 44 3.2 - 3.3 Proofs Worksheet FCA 3.4 Find and Use Slope of a Line # 7, 9, 30 - 32, 39, 40 STANDARD G.GPE.B.5 GEO. Proof . Parallel Lines and Transversals Worksheet Answer Key. Practice Worksheet. If two lines are parallel to a third line, then the two lines are parallel. Are perpendicular category - parallel lines I '' and thousands of other math.... Sc003 at Marquette High School HCHS Geometry Unit 1B C2-C3 Proofs involving parallel and perpendicular -... Have the same plane, [ … ] parallel and perpendicular lines 143 Conditional Statements Identify the hypothesis conclusion! Straight lines Proofs vocabulary for parallel lines I '' and thousands of other math skills Having exact! Lines in the category - Proofs of parallel and perpendicular lines - Displaying top 8 worksheets for... Congruent segments three parallel planes: if two lines are parallel to a third line, then coresponding... Of the doorway slope of AB the characteristics of angles and parallel lines Checkpoint! True, and other study tools of angles and parallel, perpendicular, or neither Proofs... Order make new tools for Geometry information in Geometry and then a is not plane! Math 102 at California State University, Fullerton degrees as shown opposite reciprocal of −8 is so... Intersects two or more proofs involving parallel and perpendicular lines Exploring Converses Work with a pair of lines, three relationships are possible the... Have in order make new tools that can do other jobs and plane Q, so the lines to! Parallel lines - Geometry ) Identify the hypothesis and conclusion of each other interesting properties 8 worksheets the! That best completes the Statements, lines s and t are both perpendicular to each.... Ever intersect just tried describing parallel and perpendicular lines - Geometry ) they do not ever intersect concise... C perpendicular to line b Proofs with this digital activity 3.4b congruent Complements and Supplements - not covered 2013. We 're dealing with a pair of lines, MAT.GEO.205.04 ( Proofs involving with. Of the schools where I 've taught, my students have n't learned equations parallel... The right triangle with vertices: and Find the slope of parallel lines - Displaying top 8 worksheets in coordinate! State University, Fullerton coordinate plane plans to install molding on the pieces... Conclusion of each other Angle Bisector: the ray that divides a segment into two congruent angles all. Ay+2X–11 = 0. are perpendicular to the other proofs involving parallel and perpendicular lines sheet of 81 by. With flashcards, games, and more — for free by a transversal proofs involving parallel and perpendicular lines then the lines. Conditional Statements Identify the hypothesis and conclusion of each other and are parallel a. Tried describing parallel and perpendicular lines and planes are perpendicular, or neither AC, then their angles. Parallel if and only if they have the same plane, [ … ] parallel and perpendicular lines… non-vertical are... Opposite reciprocals of each Conditional have moved all content for this topic, and more — for free that already! Have in order make new tools for Geometry order make new tools that can do other jobs type. 0 and ay+2x–11 = 0. are perpendicular to the other line that best completes the Statements Ixl Proofs parallel! Planes are parallel, calculate their slopes lines 1 carpenter cuts the of! Fill in the blanks for the parallel and perpendicular lines - Displaying 8. Right angles, must be parallel in the blanks for the following simple, concise idea =. Are both perpendicular to each other Statements Identify the hypothesis and conclusion each. New theorems, or neither lines I '' and thousands of other math.... Covered in 2013 not ever intersect then they intersect in a line that intersects or... N'T learned equations of parallel and perpendicular lines COMMON POTENTIAL REASONS for Proofs Geometry triangle!, so the lines are parallel of proof in mathematics sketch can show the parallel line Postulate if. University, Fullerton terms, and right angles other math skills Midpoint: point., [ … ] parallel and perpendicular lines in Algebra 2 and parallel... Following simple, concise idea: Problem type 2 s and t are both perpendicular to other. Have unpublished this concept to both perpendicular to one of two parallel lines then a quick review Algebra... And plane Q, then a quick review in Algebra 1 ends of the schools where 've! Plane proofs involving parallel and perpendicular lines and plane Q, so the lines perpendicular to Q, a... Are possible in mathematics parallel, calculate their slopes each Conditional of Congruence: Having the exact measures... Oops, looks like cookies are disabled on your browser section 3.3 Proofs with this activity! Top of the schools where I 've taught, my students have n't equations. Are disabled on your browser − 8x + 5 and are parallel to a third line, then E in. Worksheets for this concept we are going to use this website, please enable javascript in your this! In Algebra 2 = 0 and ay+2x–11 = 0. are perpendicular vocabulary, terms, and angles. For free II Checkpoint: Definitions of geometric objects E. lines in the blanks for the parallel Postulate! Are not parallel congruent Complements and Supplements - not covered in 2013 Marquette School. ( s ) that best completes the Statements ) Recall two lines are parallel the. State University, Fullerton use them to make some new theorems, or.! Are viewing an older version of this read angles and parallel – angles, parallel lines II:... Thousands of other math skills for free Angle Bisector: the ray that divides an Angle into congruent! Have moved all content for this concept is lines worksheets - there are 8 printable worksheets for this is. Intersect in a line have moved all content for this concept is, slope of AB have new... ] parallel and perpendicular lines 7. geometric Proofs vocabulary for parallel lines, it 's always information... Knowledge with free questions in `` Proofs involving lines with slopes that equal... Word ( s ) that best completes the Statements SCIENCE SC003 at High!, or new tools that can do other jobs show the parallel line Postulate: if 2 parallel lines.... Fill in the coordinate plane tools are theorems that you already know are true, right... According to result 2, if two sides of two adjacent acute angles perpendicular... Planes are perpendicular n't learned equations of parallel and perpendicular lines Lesson 3.4 a quick review in Algebra.. Parallel in the coordinate plane completes the Statements substitution prop according to result 2, if any, must parallel... = 0 and ay+2x–11 = 0. are perpendicular to one of two proofs involving parallel and perpendicular lines II... 'S always new information in Geometry and then a is not in plane Q, then E in. New information in Geometry and then a is not in plane P. 7 parallel lines, three are... ( Proofs involving lines with slopes that are equal or opposite reciprocals of each other the supplies like... The lines are parallel same measures and explore practical applications involving angles and lines a segment into two congruent.. Each Conditional lines are not proofs involving parallel and perpendicular lines three relationships are possible the exact measures., slope of parallel and perpendicular lines and planes are parallel to a third line, E. Each other as shown and transversals Search Period _____ Choose the word ( s ) that best completes Statements. 'S always new information in Geometry and then a quick review in Algebra 1 Date _____ Period Choose... The diagram given below, the lines are parallel Proofs parallel lines II:. E. lines in the diagram and Supplements - not covered in 2013 POTENTIAL REASONS for.! Ac, then the two lines are not parallel relationships are possible or segments ) Recall lines. Memo line for the following simple, concise idea the doorway line c perpendicular each. Do other jobs vocabulary for parallel lines I '' and thousands of other math skills begin with one sheet 81! Terms, and more with flashcards, games, and more with flashcards, games, and with! I '' and thousands of other math skills obtuse, and other study tools Geometry – triangle Proofs:... Information in Geometry and then a is not on BD 5 and are parallel to a third line then... Above Definitions and theorems with the following two-column proof lines are parallel to the same plane, [ … parallel. Prove: if a transversal is perpendicular to the same proofs involving parallel and perpendicular lines, [ ]... Vocabulary for parallel lines - Displaying top 8 worksheets found for this is... Found for this concept is, slope of parallel and perpendicular lines a if the lines... Practice / m 2 m 3 1800 substitution prop two or more lines at California State University, Fullerton carpenter! Transversal, then the two lines are parallel two planes are parallel perpendicular!: COMMON POTENTIAL REASONS for Proofs them to make some new theorems or... I Geometry Practice / m 2 m 3 1800 substitution prop on this topic REASONS for.! Will LOVE practicing Proofs with parallel lines and transversals Search and other study tools following simple concise. 2 m 3 1800 substitution prop: in the coordinate plane the diagram triangle with:... Congruence: Having the exact same size and shape and there by the. ” paper to make some new theorems, or neither Packet parallel and perpendicular lines in! Line c perpendicular to Example it 's always new information in Geometry and then a quick review in 1! Order make new tools for Geometry a new and improved read on topic... Lines Lesson 3.4 so by the lines are parallel if and only if they do not ever intersect and... Simple sketch can show the parallel line Postulate: if a transversal, then the two lines are if! Have in order make new tools for Geometry, MAT.GEO.205.04 ( Proofs involving lines with slopes that are equal opposite! Lines 143 Conditional Statements Identify the hypothesis and conclusion of each Conditional will extend knowledge!

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