CHAPTER 3 3 3 PROVING LINES PARALLEL SAT
![CHAPTER 3 3 -3 PROVING LINES PARALLEL CHAPTER 3 3 -3 PROVING LINES PARALLEL](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-1.jpg)
![SAT PROBLEM OF THE DAY • SAT PROBLEM OF THE DAY •](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-2.jpg)
![OBJECTIVES • Use the angles formed by a transversal to prove two lines are OBJECTIVES • Use the angles formed by a transversal to prove two lines are](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-3.jpg)
![CONVERSE • Recall that the converse of a theorem is found by exchanging the CONVERSE • Recall that the converse of a theorem is found by exchanging the](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-4.jpg)
![CONVERSE CONVERSE](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-5.jpg)
![EXAMPLE#1 • Use the Converse of the Corresponding Angles Postulate and the given information EXAMPLE#1 • Use the Converse of the Corresponding Angles Postulate and the given information](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-6.jpg)
![EXAMPLE#2 • Use the Converse of the Corresponding Angles Postulate and the given information EXAMPLE#2 • Use the Converse of the Corresponding Angles Postulate and the given information](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-7.jpg)
![STUDENT GUIDED PRACTICE • Do problems 1 -3 in the book page 166 STUDENT GUIDED PRACTICE • Do problems 1 -3 in the book page 166](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-8.jpg)
![PROVING LINES PARALLEL The Converse of the Corresponding Angles Postulate is used to construct PROVING LINES PARALLEL The Converse of the Corresponding Angles Postulate is used to construct](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-9.jpg)
![THEOREMS THEOREMS](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-10.jpg)
![EXAMPLE • Use the given information and theorems you have learned to show that EXAMPLE • Use the given information and theorems you have learned to show that](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-11.jpg)
![EXAMPLE • Use the given information and theorems you have learned to show that EXAMPLE • Use the given information and theorems you have learned to show that](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-12.jpg)
![CONTINUE EXAMPLE • m 2 + m 3 = 58° + 122° • = CONTINUE EXAMPLE • m 2 + m 3 = 58° + 122° • =](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-13.jpg)
![STUDENT GUIDED PRACTICE • Do problems 4 -6 in your book page 166 STUDENT GUIDED PRACTICE • Do problems 4 -6 in your book page 166](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-14.jpg)
![PROVING PARALLEL LINES • Given: p || r , 1 3 • Prove: ℓ PROVING PARALLEL LINES • Given: p || r , 1 3 • Prove: ℓ](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-15.jpg)
![SOLUTION • statements 1. p || r reasons 1. Given 2. 3 2 2. SOLUTION • statements 1. p || r reasons 1. Given 2. 3 2 2.](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-16.jpg)
![EXAMPLE • Given: 1 4, 3 and 4 are supplementary. • Prove: ℓ || EXAMPLE • Given: 1 4, 3 and 4 are supplementary. • Prove: ℓ ||](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-17.jpg)
![SOLUTION Statements 1. 1 4 2. m 1 = m 4 3. 3 and SOLUTION Statements 1. 1 4 2. m 1 = m 4 3. 3 and](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-18.jpg)
![APPLICATION • A carpenter is creating a woodwork pattern and wants two long pieces APPLICATION • A carpenter is creating a woodwork pattern and wants two long pieces](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-19.jpg)
![• A line through the center of the horizontal piece forms a transversal • A line through the center of the horizontal piece forms a transversal](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-20.jpg)
![• • m 1 = 8 x + 20 = 8(15) + 20 • • m 1 = 8 x + 20 = 8(15) + 20](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-21.jpg)
![APPLICATION • What if…? Suppose the corresponding angles on the opposite side of the APPLICATION • What if…? Suppose the corresponding angles on the opposite side of the](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-22.jpg)
![CONTINUE • 4 y – 2 = 4(8) – 2 = 30° 3 y CONTINUE • 4 y – 2 = 4(8) – 2 = 30° 3 y](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-23.jpg)
![HOMEWORK!!! • Do problems 12 -18 and problem 22 in your book page 166 HOMEWORK!!! • Do problems 12 -18 and problem 22 in your book page 166](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-24.jpg)
![CLOSURE • Today we learned about parallel lines • Next class we are going CLOSURE • Today we learned about parallel lines • Next class we are going](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-25.jpg)
- Slides: 25
![CHAPTER 3 3 3 PROVING LINES PARALLEL CHAPTER 3 3 -3 PROVING LINES PARALLEL](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-1.jpg)
CHAPTER 3 3 -3 PROVING LINES PARALLEL
![SAT PROBLEM OF THE DAY SAT PROBLEM OF THE DAY •](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-2.jpg)
SAT PROBLEM OF THE DAY •
![OBJECTIVES Use the angles formed by a transversal to prove two lines are OBJECTIVES • Use the angles formed by a transversal to prove two lines are](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-3.jpg)
OBJECTIVES • Use the angles formed by a transversal to prove two lines are parallel.
![CONVERSE Recall that the converse of a theorem is found by exchanging the CONVERSE • Recall that the converse of a theorem is found by exchanging the](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-4.jpg)
CONVERSE • Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.
![CONVERSE CONVERSE](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-5.jpg)
CONVERSE
![EXAMPLE1 Use the Converse of the Corresponding Angles Postulate and the given information EXAMPLE#1 • Use the Converse of the Corresponding Angles Postulate and the given information](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-6.jpg)
EXAMPLE#1 • Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. 4 8 4 and 8 are corresponding angles. ℓ || m Conv. of Corr. s Post.
![EXAMPLE2 Use the Converse of the Corresponding Angles Postulate and the given information EXAMPLE#2 • Use the Converse of the Corresponding Angles Postulate and the given information](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-7.jpg)
EXAMPLE#2 • Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m 3 = (4 x – 80)°, m 7 = (3 x – 50)°, x = 30 m 3 = 4(30) – 80 = 40 for x. Substitute 30 m 7 = 3(30) – 50 = 40 Substitute 30 • m 3 = m 7 Trans. Prop. for x. • 3 7 Def. of s. • ℓ || m Conv. of Corr. s of Equality
![STUDENT GUIDED PRACTICE Do problems 1 3 in the book page 166 STUDENT GUIDED PRACTICE • Do problems 1 -3 in the book page 166](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-8.jpg)
STUDENT GUIDED PRACTICE • Do problems 1 -3 in the book page 166
![PROVING LINES PARALLEL The Converse of the Corresponding Angles Postulate is used to construct PROVING LINES PARALLEL The Converse of the Corresponding Angles Postulate is used to construct](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-9.jpg)
PROVING LINES PARALLEL The Converse of the Corresponding Angles Postulate is used to construct parallel lines. The Parallel Postulate guarantees that for any line ℓ, you can always construct a parallel line through a point that is not on ℓ.
![THEOREMS THEOREMS](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-10.jpg)
THEOREMS
![EXAMPLE Use the given information and theorems you have learned to show that EXAMPLE • Use the given information and theorems you have learned to show that](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-11.jpg)
EXAMPLE • Use the given information and theorems you have learned to show that r || s. 4 8 4 and 8 are alternate exterior angles. r || s Conv. Of Alt. Ext. s Thm.
![EXAMPLE Use the given information and theorems you have learned to show that EXAMPLE • Use the given information and theorems you have learned to show that](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-12.jpg)
EXAMPLE • Use the given information and theorems you have learned to show that r || s. m 2 = (10 x + 8)°, m 3 = (25 x – 3)°, x = 5 m 2 = 10 x + 8 = 10(5) + 8 = 58 Substitute 5 for x. • m 3 = 25 x – 3 • = 25(5) – 3 = 122 Substitute 5 for x.
![CONTINUE EXAMPLE m 2 m 3 58 122 CONTINUE EXAMPLE • m 2 + m 3 = 58° + 122° • =](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-13.jpg)
CONTINUE EXAMPLE • m 2 + m 3 = 58° + 122° • = 180° 2 and 3 are same-side interior angles. • r || s Conv. of Same-Side Int. s Thm.
![STUDENT GUIDED PRACTICE Do problems 4 6 in your book page 166 STUDENT GUIDED PRACTICE • Do problems 4 -6 in your book page 166](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-14.jpg)
STUDENT GUIDED PRACTICE • Do problems 4 -6 in your book page 166
![PROVING PARALLEL LINES Given p r 1 3 Prove ℓ PROVING PARALLEL LINES • Given: p || r , 1 3 • Prove: ℓ](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-15.jpg)
PROVING PARALLEL LINES • Given: p || r , 1 3 • Prove: ℓ || m
![SOLUTION statements 1 p r reasons 1 Given 2 3 2 2 SOLUTION • statements 1. p || r reasons 1. Given 2. 3 2 2.](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-16.jpg)
SOLUTION • statements 1. p || r reasons 1. Given 2. 3 2 2. Alt. Ext. s Thm. 3. 1 3 3. Given 4. 1 2 5. ℓ ||m 4. Trans. Prop. of 5. Conv. of Corr. s Post.
![EXAMPLE Given 1 4 3 and 4 are supplementary Prove ℓ EXAMPLE • Given: 1 4, 3 and 4 are supplementary. • Prove: ℓ ||](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-17.jpg)
EXAMPLE • Given: 1 4, 3 and 4 are supplementary. • Prove: ℓ || m
![SOLUTION Statements 1 1 4 2 m 1 m 4 3 3 and SOLUTION Statements 1. 1 4 2. m 1 = m 4 3. 3 and](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-18.jpg)
SOLUTION Statements 1. 1 4 2. m 1 = m 4 3. 3 and 4 are supp. 4. m 3 + m 4 = 180 5. m 3 + m 1 = 180 6. m 2 = m 3 7. m 2 + m 1 = 180 8. ℓ || m Reasons 1. Given 2. Def. s 3. Given 4. Trans. Prop. of 5. Substitution 6. Vert. s Thm. 7. Substitution 8. Conv. of Same-Side Interior s Post.
![APPLICATION A carpenter is creating a woodwork pattern and wants two long pieces APPLICATION • A carpenter is creating a woodwork pattern and wants two long pieces](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-19.jpg)
APPLICATION • A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m 1= (8 x + 20)° and m 2 = (2 x + 10)°. If x = 15, show that pieces A and B are parallel.
![A line through the center of the horizontal piece forms a transversal • A line through the center of the horizontal piece forms a transversal](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-20.jpg)
• A line through the center of the horizontal piece forms a transversal to pieces A and B. • 1 and 2 are same-side interior angles. If 1 and 2 are supplementary, then pieces A and B are parallel. • Substitute 15 for x in each expression.
![m 1 8 x 20 815 20 • • m 1 = 8 x + 20 = 8(15) + 20](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-21.jpg)
• • m 1 = 8 x + 20 = 8(15) + 20 = 140 m 2 = 2 x + 10 = 2(15) + 10 = 40 m 1+m 2 = 140 + 40 = 180 The same-side interior angles are supplementary, so pieces A and B are parallel by the Converse of the Same -Side Interior Angles Theorem.
![APPLICATION What if Suppose the corresponding angles on the opposite side of the APPLICATION • What if…? Suppose the corresponding angles on the opposite side of the](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-22.jpg)
APPLICATION • What if…? Suppose the corresponding angles on the opposite side of the boat measure (4 y – 2)° and (3 y + 6)°, where • y = 8. Show that the oars are parallel.
![CONTINUE 4 y 2 48 2 30 3 y CONTINUE • 4 y – 2 = 4(8) – 2 = 30° 3 y](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-23.jpg)
CONTINUE • 4 y – 2 = 4(8) – 2 = 30° 3 y + 6 = 3(8) + 6 = 30° • The angles are congruent, so the oars are || by the Conv. of the Corr. s Post.
![HOMEWORK Do problems 12 18 and problem 22 in your book page 166 HOMEWORK!!! • Do problems 12 -18 and problem 22 in your book page 166](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-24.jpg)
HOMEWORK!!! • Do problems 12 -18 and problem 22 in your book page 166 and 167
![CLOSURE Today we learned about parallel lines Next class we are going CLOSURE • Today we learned about parallel lines • Next class we are going](https://slidetodoc.com/presentation_image/52dafcd80b97663566cd676068319f6b/image-25.jpg)
CLOSURE • Today we learned about parallel lines • Next class we are going to learned about perpendicular lines
Geometry proving lines parallel
Proving lines parallel assignment
Corresponding angles flow proof
Proving lines parallel with algebra
3-3 proving lines parallel part 1 answers
Lesson 3-5 proving lines parallel answers
Proving lines are parallel worksheet answers 14-3
3-3 proving lines parallel
3-5 proving lines parallel answers
Transversal guided notes
7-2 proving lines are parallel
Lesson 3-5 proving lines parallel
3-5 proving lines parallel
Proving lines parallel worksheet 3-3
Lesson 4-3 proving lines are parallel
3-3 proving parallel lines
Focal points n fingerprint pattern
Define parallel lines and intersecting lines
Chapter 3 parallel and perpendicular lines
Chapter 3 parallel and perpendicular lines
Chapter 3 quiz geometry answers
Chapter 3-2 angles and parallel lines
Geometry chapter 3 review parallel and perpendicular lines
Chapter 2 parallel lines
Unit 4 congruent triangles homework 3
How to find the resultant of two parallel forces