3 3 Proving Lines Parallel Warm Up Identify
![3 -3 Proving Lines Parallel Warm Up Identify each angle pair. 1. 1 and 3 -3 Proving Lines Parallel Warm Up Identify each angle pair. 1. 1 and](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-1.jpg)
![3 -3 Proving Lines Parallel Objective Use the angles formed by a transversal to 3 -3 Proving Lines Parallel Objective Use the angles formed by a transversal to](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-2.jpg)
![3 -3 Proving Lines Parallel Holt Geometry 3 -3 Proving Lines Parallel Holt Geometry](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-3.jpg)
![3 -3 Proving Lines Parallel Example 1 A: Using the Converse of the Corresponding 3 -3 Proving Lines Parallel Example 1 A: Using the Converse of the Corresponding](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-4.jpg)
![3 -3 Proving Lines Parallel Example 1 B: Using the Converse of the Corresponding 3 -3 Proving Lines Parallel Example 1 B: Using the Converse of the Corresponding](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-5.jpg)
![3 -3 Proving Lines Parallel Check It Out! Example 1 a Use the Converse 3 -3 Proving Lines Parallel Check It Out! Example 1 a Use the Converse](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-6.jpg)
![3 -3 Proving Lines Parallel Check It Out! Example 1 b Use the Converse 3 -3 Proving Lines Parallel Check It Out! Example 1 b Use the Converse](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-7.jpg)
![3 -3 Proving Lines Parallel The Converse of the Corresponding Angles Postulate is used 3 -3 Proving Lines Parallel The Converse of the Corresponding Angles Postulate is used](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-8.jpg)
![3 -3 Proving Lines Parallel Holt Geometry 3 -3 Proving Lines Parallel Holt Geometry](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-9.jpg)
![3 -3 Proving Lines Parallel Example 2 A: Determining Whether Lines are Parallel Use 3 -3 Proving Lines Parallel Example 2 A: Determining Whether Lines are Parallel Use](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-10.jpg)
![3 -3 Proving Lines Parallel Example 2 B: Determining Whether Lines are Parallel Use 3 -3 Proving Lines Parallel Example 2 B: Determining Whether Lines are Parallel Use](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-11.jpg)
![3 -3 Proving Lines Parallel Example 2 B Continued Use the given information and 3 -3 Proving Lines Parallel Example 2 B Continued Use the given information and](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-12.jpg)
![3 -3 Proving Lines Parallel Check It Out! Example 2 a Refer to the 3 -3 Proving Lines Parallel Check It Out! Example 2 a Refer to the](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-13.jpg)
![3 -3 Proving Lines Parallel Check It Out! Example 2 b Refer to the 3 -3 Proving Lines Parallel Check It Out! Example 2 b Refer to the](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-14.jpg)
![3 -3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r 3 -3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-15.jpg)
![3 -3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r 3 -3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-16.jpg)
![3 -3 Proving Lines Parallel Check It Out! Example 3 Given: 1 4, 3 3 -3 Proving Lines Parallel Check It Out! Example 3 Given: 1 4, 3](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-17.jpg)
![3 -3 Proving Lines Parallel Check It Out! Example 3 Continued Statements Reasons 1. 3 -3 Proving Lines Parallel Check It Out! Example 3 Continued Statements Reasons 1.](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-18.jpg)
![3 -3 Proving Lines Parallel Example 4: Carpentry Application A carpenter is creating a 3 -3 Proving Lines Parallel Example 4: Carpentry Application A carpenter is creating a](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-19.jpg)
![3 -3 Proving Lines Parallel Example 4 Continued A line through the center of 3 -3 Proving Lines Parallel Example 4 Continued A line through the center of](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-20.jpg)
![3 -3 Proving Lines Parallel Example 4 Continued m 1 = 8 x + 3 -3 Proving Lines Parallel Example 4 Continued m 1 = 8 x +](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-21.jpg)
![3 -3 Proving Lines Parallel Check It Out! Example 4 What if…? Suppose the 3 -3 Proving Lines Parallel Check It Out! Example 4 What if…? Suppose the](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-22.jpg)
![3 -3 Proving Lines Parallel Homework: p. 166 -169, #12 -22 Even, 24 -31, 3 -3 Proving Lines Parallel Homework: p. 166 -169, #12 -22 Even, 24 -31,](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-23.jpg)
- Slides: 23
![3 3 Proving Lines Parallel Warm Up Identify each angle pair 1 1 and 3 -3 Proving Lines Parallel Warm Up Identify each angle pair. 1. 1 and](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-1.jpg)
3 -3 Proving Lines Parallel Warm Up Identify each angle pair. 1. 1 and 3 corr. s 2. 3 and 6 alt. int. s 3. 4 and 5 alt. ext. s 4. 6 and 7 same-side int s Holt Geometry
![3 3 Proving Lines Parallel Objective Use the angles formed by a transversal to 3 -3 Proving Lines Parallel Objective Use the angles formed by a transversal to](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-2.jpg)
3 -3 Proving Lines Parallel Objective Use the angles formed by a transversal to prove two lines are parallel. Holt Geometry
![3 3 Proving Lines Parallel Holt Geometry 3 -3 Proving Lines Parallel Holt Geometry](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-3.jpg)
3 -3 Proving Lines Parallel Holt Geometry
![3 3 Proving Lines Parallel Example 1 A Using the Converse of the Corresponding 3 -3 Proving Lines Parallel Example 1 A: Using the Converse of the Corresponding](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-4.jpg)
3 -3 Proving Lines Parallel Example 1 A: 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. 4 8 ℓ || m Holt Geometry 4 and 8 are corresponding angles. Conv. of Corr. s Post.
![3 3 Proving Lines Parallel Example 1 B Using the Converse of the Corresponding 3 -3 Proving Lines Parallel Example 1 B: Using the Converse of the Corresponding](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-5.jpg)
3 -3 Proving Lines Parallel Example 1 B: 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. m 3 = (4 x – 80)°, m 7 = (3 x – 50)°, x = 30 m 3 = 4(30) – 80 = 40 m 8 = 3(30) – 50 = 40 m 3 = m 8 3 8 ℓ || m Holt Geometry Substitute 30 for x. Trans. Prop. of Equality Def. of s. Conv. of Corr. s Post.
![3 3 Proving Lines Parallel Check It Out Example 1 a Use the Converse 3 -3 Proving Lines Parallel Check It Out! Example 1 a Use the Converse](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-6.jpg)
3 -3 Proving Lines Parallel Check It Out! Example 1 a 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 Geometry 1 and 3 are corresponding angles. Conv. of Corr. s Post.
![3 3 Proving Lines Parallel Check It Out Example 1 b Use the Converse 3 -3 Proving Lines Parallel Check It Out! Example 1 b Use the Converse](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-7.jpg)
3 -3 Proving Lines Parallel Check It Out! Example 1 b Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m 7 = (4 x + 25)°, m 5 = (5 x + 12)°, x = 13 m 7 = 4(13) + 25 = 77 m 5 = 5(13) + 12 = 77 m 7 = m 5 7 5 ℓ || m Holt Geometry Substitute 13 for x. Trans. Prop. of Equality Def. of s. Conv. of Corr. s Post.
![3 3 Proving Lines Parallel The Converse of the Corresponding Angles Postulate is used 3 -3 Proving Lines Parallel The Converse of the Corresponding Angles Postulate is used](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-8.jpg)
3 -3 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. Holt Geometry
![3 3 Proving Lines Parallel Holt Geometry 3 -3 Proving Lines Parallel Holt Geometry](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-9.jpg)
3 -3 Proving Lines Parallel Holt Geometry
![3 3 Proving Lines Parallel Example 2 A Determining Whether Lines are Parallel Use 3 -3 Proving Lines Parallel Example 2 A: Determining Whether Lines are Parallel Use](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-10.jpg)
3 -3 Proving Lines Parallel Example 2 A: Determining Whether Lines are Parallel 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. Int. s Thm. Holt Geometry
![3 3 Proving Lines Parallel Example 2 B Determining Whether Lines are Parallel Use 3 -3 Proving Lines Parallel Example 2 B: Determining Whether Lines are Parallel Use](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-11.jpg)
3 -3 Proving Lines Parallel Example 2 B: Determining Whether Lines are Parallel 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. Holt Geometry
![3 3 Proving Lines Parallel Example 2 B Continued Use the given information and 3 -3 Proving Lines Parallel Example 2 B Continued Use the given information and](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-12.jpg)
3 -3 Proving Lines Parallel Example 2 B Continued 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 + m 3 = 58° + 122° = 180° r || s Holt 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 2 a Refer to the 3 -3 Proving Lines Parallel Check It Out! Example 2 a Refer to the](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-13.jpg)
3 -3 Proving Lines Parallel Check It Out! Example 2 a Refer to the diagram. Use the given information and theorems you have learned to show that r || s. m 4 = m 8 4 8 Congruent angles 4 8 4 and 8 are alternate exterior angles. r || s Conv. of Alt. Int. s Thm. Holt Geometry
![3 3 Proving Lines Parallel Check It Out Example 2 b Refer to the 3 -3 Proving Lines Parallel Check It Out! Example 2 b Refer to the](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-14.jpg)
3 -3 Proving Lines Parallel Check It Out! Example 2 b Refer to the diagram. Use the given information and theorems you have learned to show that r || s. m 3 = 2 x , m 7 = (x + 50) , x = 50 m 3 = 2 x = 2(50) = 100° Substitute 50 for x. m 7 = x + 50 = 50 + 50 = 100° Substitute 5 for x. m 3 = 100 and m 7 = 100 3 7 r||s Conv. of the Alt. Int. s Thm. Holt Geometry
![3 3 Proving Lines Parallel Example 3 Proving Lines Parallel Given p r 3 -3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-15.jpg)
3 -3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r , 1 3 Prove: ℓ || m Holt Geometry
![3 3 Proving Lines Parallel Example 3 Continued Statements Reasons 1 p r 3 -3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-16.jpg)
3 -3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r 1. Given 2. 3 2 2. Alt. Ext. s Thm. 3. 1 3 3. Given 4. 1 2 4. Trans. Prop. of 5. ℓ ||m 5. Conv. of Corr. s Post. Holt Geometry
![3 3 Proving Lines Parallel Check It Out Example 3 Given 1 4 3 3 -3 Proving Lines Parallel Check It Out! Example 3 Given: 1 4, 3](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-17.jpg)
3 -3 Proving Lines Parallel Check It Out! Example 3 Given: 1 4, 3 and 4 are supplementary. Prove: ℓ || m Holt Geometry
![3 3 Proving Lines Parallel Check It Out Example 3 Continued Statements Reasons 1 3 -3 Proving Lines Parallel Check It Out! Example 3 Continued Statements Reasons 1.](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-18.jpg)
3 -3 Proving Lines Parallel Check It Out! Example 3 Continued Statements Reasons 1. 1 4 2. m 1 = m 4 1. Given 2. Def. s 3. 4. 5. 6. 7. 3. Given 4. Trans. Prop. of 3 and 4 are supp. m 3 + m 4 = 180 m 3 + m 1 = 180 m 2 = m 3 m 2 + m 1 = 180 8. ℓ || m Holt Geometry 5. Substitution 6. Vert. s Thm. 7. Substitution 8. Conv. of Same-Side Interior s Post.
![3 3 Proving Lines Parallel Example 4 Carpentry Application A carpenter is creating a 3 -3 Proving Lines Parallel Example 4: Carpentry Application A carpenter is creating a](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-19.jpg)
3 -3 Proving Lines Parallel Example 4: Carpentry 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. Holt Geometry
![3 3 Proving Lines Parallel Example 4 Continued A line through the center of 3 -3 Proving Lines Parallel Example 4 Continued A line through the center of](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-20.jpg)
3 -3 Proving Lines Parallel Example 4 Continued 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. Holt Geometry
![3 3 Proving Lines Parallel Example 4 Continued m 1 8 x 3 -3 Proving Lines Parallel Example 4 Continued m 1 = 8 x +](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-21.jpg)
3 -3 Proving Lines Parallel Example 4 Continued m 1 = 8 x + 20 = 8(15) + 20 = 140 Substitute 15 for x. m 2 = 2 x + 10 = 2(15) + 10 = 40 m 1+m 2 = 140 + 40 = 180 Substitute 15 for x. 1 and 2 are supplementary. The same-side interior angles are supplementary, so pieces A and B are parallel by the Converse of the Same-Side Interior Angles Theorem. Holt Geometry
![3 3 Proving Lines Parallel Check It Out Example 4 What if Suppose the 3 -3 Proving Lines Parallel Check It Out! Example 4 What if…? Suppose the](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-22.jpg)
3 -3 Proving Lines Parallel Check It Out! Example 4 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. 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. Holt Geometry
![3 3 Proving Lines Parallel Homework p 166 169 12 22 Even 24 31 3 -3 Proving Lines Parallel Homework: p. 166 -169, #12 -22 Even, 24 -31,](https://slidetodoc.com/presentation_image_h2/3ba11715e4078df4a5e5ec6772f3b67a/image-23.jpg)
3 -3 Proving Lines Parallel Homework: p. 166 -169, #12 -22 Even, 24 -31, 34, 35, 38, 40, 41, 55, 56, 60 Holt Geometry
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