Proving lines parallel
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This document discusses proving that two lines are parallel using angles formed by a transversal. It provides examples of using the converse of corresponding angles, alternate interior angles, same-side interior angles, and vertical angles postulates and theorems to show parallel lines. The document also includes warm up questions asking students to write the converse of statements and a lesson quiz to assess understanding.
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This document discusses using angle relationships to prove that two lines are parallel. It provides examples of using the converse of corresponding angles, alternate interior angles, same-side interior angles, and alternate exterior angles postulates and theorems to show parallel lines. The examples include solving equations to determine if specific angle measures are equal, indicating the lines are parallel. The document also discusses using these concepts to solve a problem about ensuring parallel pieces of wood in a carpentry application.
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Proving Lines Parallel Lesson Presentation.ppt
Use the given information and the theorems you have learned to show that r || s.
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.
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.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
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
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
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.
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.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
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
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
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.
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.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
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
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
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.
Recall that the conver
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This document discusses proving that two lines are parallel using theorems about angles formed when a transversal crosses the lines. It provides examples of using the converse of corresponding angles, alternate interior angles, same-side interior angles, and alternate exterior angles postulates/theorems to show that lines are parallel given information about the angles. It also includes examples applying these concepts to solve geometry problems and prove lines are parallel in practical applications like carpentry.
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Proving Lines Parallel Lesson Presentation.ppt
Use the given information and the theorems you have learned to show that r || s.
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.
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.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
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
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
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.
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.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
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
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
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.
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.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
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
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
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.
Recall that the conver
Geometry 201 unit 3.3
This document discusses proving that two lines are parallel using theorems about angles formed when a transversal crosses the lines. It provides examples of using the converse of corresponding angles, alternate interior angles, same-side interior angles, and alternate exterior angles postulates/theorems to show that lines are parallel given information about the angles. It also includes examples applying these concepts to solve geometry problems and prove lines are parallel in practical applications like carpentry.
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This document contains examples and explanations about perpendicular lines from a geometry textbook. It includes examples of finding the shortest distance from a point to a line by drawing a perpendicular segment, proofs about perpendicular lines, and applications of perpendicular lines in carpentry and swimming. The document contains instructions for students to complete homework problems on these concepts.
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This document contains a geometry drill with examples and explanations of perpendicular lines. It begins with warm up problems solving inequalities and equations. It then covers the key concepts that the perpendicular bisector of a segment is perpendicular to the segment at its midpoint, and the shortest distance from a point to a line is the perpendicular segment. Examples demonstrate writing proofs about perpendicular and parallel lines and applying the concept to carpentry. The homework assigned is to complete problems from the textbook.
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This document contains a geometry drill with examples and explanations of perpendicular lines. It begins with warm up problems solving inequalities and equations. It then covers the key concepts that the perpendicular bisector of a segment is perpendicular to the segment at its midpoint, and the shortest distance from a point to a line is the perpendicular segment. Examples demonstrate writing proofs about perpendicular and parallel lines and applying the concept to carpentry. The homework assigned is to complete problems from the textbook.
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This document provides examples and explanations about parallel and perpendicular lines. It defines parallel lines as lines in the same plane that do not intersect. Perpendicular lines intersect to form a 90 degree angle. Several examples show how to identify parallel and perpendicular lines based on their slopes. The document also demonstrates applications to geometry, such as showing when a figure like a parallelogram or right triangle is formed based on the relationships between line slopes.
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This document discusses proving that quadrilaterals are parallelograms using various theorems and properties of parallelograms. It provides examples of showing quadrilateral figures are parallelograms by proving pairs of opposite sides are parallel, pairs of angles are supplementary, or the diagonals of the figure bisect each other. The document also discusses determining if given information is sufficient to classify a quadrilateral as a parallelogram and applying properties of parallelograms to real world examples.
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Proving lines parallel
- 1. Holt Geometry 3-3 Proving Lines Parallel3-3 Proving Lines Parallel Holt Geometry
- 2. Holt Geometry 3-3 Proving Lines Parallel Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC = AC, then A, B, and C are collinear. If a + c = b + c, then a = b. If A and B are complementary, then mA + mB =90°. If A, B, and C are collinear, then AB + BC = AC.
- 3. Holt Geometry 3-3 Proving Lines Parallel Use the angles formed by a transversal to prove two lines are parallel. Objective
- 4. Holt Geometry 3-3 Proving Lines Parallel 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.
- 5. Holt Geometry 3-3 Proving Lines Parallel
- 6. Holt Geometry 3-3 Proving Lines Parallel Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. 4 8 4 8 4 and 8 are corresponding angles. ℓ || m Conv. of Corr. s Post.
- 7. Holt Geometry 3-3 Proving Lines Parallel Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. Example 1B: Using the Converse of the Corresponding Angles Postulate m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30 m3 = 4(30) – 80 = 40 Substitute 30 for x. m7 = 3(30) – 50 = 40 Substitute 30 for x. ℓ || m Conv. of Corr. s Post. 3 7 Def. of s. m3 = m7 Trans. Prop. of Equality
- 8. Holt Geometry 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.
- 9. Holt Geometry 3-3 Proving Lines Parallel
- 10. Holt Geometry 3-3 Proving Lines Parallel Use the given information and the theorems you have learned to show that r || s. Example 2A: Determining Whether Lines are Parallel 4 8
- 11. Holt Geometry 3-3 Proving Lines Parallel m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5 Use the given information and the theorems you have learned to show that r || s. Example 2B: Determining Whether Lines are Parallel m2 = 10x + 8 = 10(5) + 8 = 58 Substitute 5 for x. m3 = 25x – 3 = 25(5) – 3 = 122 Substitute 5 for x.
- 12. Holt Geometry 3-3 Proving Lines Parallel m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5 Use the given information and the theorems you have learned to show that r || s. Example 2B Continued r || s Conv. of Same-Side Int. s Thm. m2 + m3 = 58° + 122° = 180° 2 and 3 are same-side interior angles.
- 13. Holt Geometry 3-3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r , 1 3 Prove: ℓ || m
- 14. Holt Geometry 3-3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r 5. ℓ ||m 2. 3 2 3. 1 3 4. 1 2 2. Alt. Ext. s Thm. 1. Given 3. Given 4. Trans. Prop. of 5. Conv. of Corr. s Post.
- 15. Holt Geometry 3-3 Proving Lines Parallel Check It Out! Example 3 Given: 1 4, 3 and 4 are supplementary. Prove: ℓ || m
- 16. Holt Geometry 3-3 Proving Lines Parallel Check It Out! Example 3 Continued Statements Reasons 1. 1 4 1. Given 2. m1 = m4 2. Def. s 3. 3 and 4 are supp. 3. Given 4. m3 + m4 = 180 4. Trans. Prop. of 5. m3 + m1 = 180 5. Substitution 6. m2 = m3 6. Vert.s Thm. 7. m2 + m1 = 180 7. Substitution 8. ℓ || m 8. Conv. of Same-Side Interior s Post.
- 17. Holt Geometry 3-3 Proving Lines Parallel Lesson Quiz: Part I Name the postulate or theorem that proves p || r. 1. 4 5 Conv. of Alt. Int. s Thm. 2. 2 7 Conv. of Alt. Ext. s Thm. 3. 3 7 Conv. of Corr. s Post. 4. 3 and 5 are supplementary. Conv. of Same-Side Int. s Thm.
- 18. Holt Geometry 3-3 Proving Lines Parallel Lesson Quiz: Part II Use the theorems and given information to prove p || r. 5. m2 = (5x + 20)°, m 7 = (7x + 8)°, and x = 6 m2 = 5(6) + 20 = 50° m7 = 7(6) + 8 = 50° m2 = m7, so 2 ≅ 7 p || r by the Conv. of Alt. Ext. s Thm.