text: Home > Grade 8 > Geometry
  
  # Geometry
  
  ## Triangle Sum Theorem
  
  Directions: Using the digits 1-9 at most one time each, fill in the blanks so that when you solve for x, it is a whole number. Source: Franco D. Adkins
  
  ## Parallel and Perpendicular Lines
  
  Directions: Using the digits 0 to 9, at most once each time, fill in blanks to create a set of 4 points that create either parallel or perpendicular lines, depending on how you connect them. ( ___, ___ ) ( ___, ___ ) ( ___, ___ ) ( ___, ___ ) Source: Bryan Anderson
  
  ## Interior Angles
  
  Directions: Using the digits 0 through 9 at most one time, fill in the boxes to make the sum of the interior angles of a triangle. Source: Ashley Henderson
  
  ## Pythagorean Theorem 2
  
  Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to find the lengths of the missing sides such that the missing leg’s length is as long as possible. Source: Robert Kaplinsky
  
  ## Pythagorean Theorem
  
  Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to find two pairs of possible lengths for the missing sides. Source: Robert Kaplinsky
  
  ## Partitioning a Line Segment
  
  Directions: Using the digits 1 to 8 exactly one time each, fill in the boxes to create a line segment AB, where between point A and point B, there exists a point P so that it partitions line segment AB into a ratio. Source: Jon Henderson
  
  ## Maximizing Volume of a Cylinder, Given Lateral Area
  
  Directions: Find at least 3 possible measures for the height and the radius of a cylinder with a lateral area of 144pi square centimeters. Which of your dimensions will give you the largest volume? Source: Jason Miller
  
  ## Perimeter and Pythagorean Theorem
  
  Directions: What could the lengths of the legs be such that the lengths of the legs are integers and x is an irrational number between 5 and 7? Source: Daniel Luevanos
explanation: The document contains multiple math problems related to geometry, including the Triangle Sum Theorem, Parallel and Perpendicular Lines, Interior Angles, Pythagorean Theorem, Partitioning a Line Segment, Maximizing Volume of a Cylinder, and Perimeter and Pythagorean Theorem. Each problem provides directions and constraints for solving the problem, but none of them include answers.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Home > Grade 8 > Geometry
  
  # Geometry
  
  ## Triangle Sum Theorem
  
  Directions: Using the digits 1-9 at most one time each, fill in the blanks so that when you solve for x, it is a whole number. Source: Franco D. Adkins
  
  ## Parallel and Perpendicular Lines
  
  Directions: Using the digits 0 to 9, at most once each time, fill in blanks to create a set of 4 points that create either parallel or perpendicular lines, depending on how you connect them. ( ___, ___ ) ( ___, ___ ) ( ___, ___ ) ( ___, ___ ) Source: Bryan Anderson
  
  ## Interior Angles
  
  Directions: Using the digits 0 through 9 at most one time, fill in the boxes to make the sum of the interior angles of a triangle. Source: Ashley Henderson
  
  ## Pythagorean Theorem 2
  
  Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to find the lengths of the missing sides such that the missing leg’s length is as long as possible. Source: Robert Kaplinsky
  
  ## Pythagorean Theorem
  
  Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to find two pairs of possible lengths for the missing sides. Source: Robert Kaplinsky
  
  ## Partitioning a Line Segment
  
  Directions: Using the digits 1 to 8 exactly one time each, fill in the boxes to create a line segment AB, where between point A and point B, there exists a point P so that it partitions line segment AB into a ratio. Source: Jon Henderson
  
  ## Maximizing Volume of a Cylinder, Given Lateral Area
  
  Directions: Find at least 3 possible measures for the height and the radius of a cylinder with a lateral area of 144pi square centimeters. Which of your dimensions will give you the largest volume? Source: Jason Miller
  
  ## Perimeter and Pythagorean Theorem
  
  Directions: What could the lengths of the legs be such that the lengths of the legs are integers and x is an irrational number between 5 and 7? Source: Daniel Luevanos
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains multiple math problems related to geometry, including the Triangle Sum Theorem, Parallel and Perpendicular Lines, Interior Angles, Pythagorean Theorem, Partitioning a Line Segment, Maximizing Volume of a Cylinder, and Perimeter and Pythagorean Theorem. Each problem provides directions and constraints for solving the problem, but none of them include answers.
  
  Label: multiple-question