United University

Geometry Grade 10. Perpendicularity of lines and planes in space Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 20 hours

This interactive course introduces 10th-grade students to the concepts of perpendicularity in solid geometry. It offers a structured exploration of essential topics, including the relationships between perpendicular lines and planes, dihedral angles, the theorem of three perpendiculars, and the measurement of distances and angles in space. Through interactive problem-solving and practice exercises, students will strengthen their understanding of three-dimensional geometric relationships.

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This interactive course introduces 10th-grade students to the concepts of perpendicularity in solid geometry. It offers a structured exploration of essential topics, including the relationships between perpendicular lines and planes, dihedral angles, the theorem of three perpendiculars, and the measurement of distances and angles in space. Through interactive problem-solving and practice exercises, students will strengthen their understanding of three-dimensional geometric relationships.

Key Features of the Course

  • Interactive learning through problem-solving tasks and exercises
  • Development of analytical and spatial reasoning skills
  • Aligned with national curriculum standards in mathematics
  • Engaging review tasks and independent assignments for consolidation

Course Modules

Module 1: Perpendicularity of Lines and Planes in Space

  • Lesson 8: Perpendicularity of Lines in Space. Perpendicularity of a Line and a Plane
  • Solve problems and complete exercises 8.1 - 8.30
  • Solve problems and complete exercises 8.31 - 8.62
  • Test your competence
  • Lesson 9: Perpendicular and a Slant. The Theorem of Three Perpendiculars
  • Solve problems and complete exercises 9.1 - 9.32
  • Solve problems and complete exercises 9.33 - 9.81
  • Test your competence
  • Independent Homework #4
  • Complete the tests
  • Review tasks for §§ 8-9
  • Complete the tasks
  • Lesson 10: Dihedral Angle. Perpendicularity of Planes
  • Solve problems and complete exercises 10.1 - 10.38
  • Solve problems and complete exercises 10.39 - 10.62
  • Test your competence
  • Lesson 11: Distances in Space
  • Solve problems and complete exercises 11.1 - 11.49
  • Solve problems and complete exercises 11.50 - 11.75
  • Solve problems and complete exercises 11.76 - 11.101
  • Test your competence
  • Lesson 12: Measurement of Angles in Space. Orthogonal Projection
  • Solve problems and complete exercises 12-1 - 12-29
  • Solve problems and complete exercises 12-30 - 12-60
  • Solve problems and complete exercises 12-61 - 12-85
  • Solve problems and complete exercises 12-86 - 12-105
  • Test your competence
  • Independent Homework #5
  • Complete the tests
  • Review tasks for §§ 10-12
  • Complete the tasks
  • Review Exercises for Section 3

Expected Learning Outcomes

  • Establishes and justifies the perpendicularity of lines, a line and a plane, and two planes.
  • Formulates the definitions of the angle between lines, a line and a plane, and planes; as well as the theorem of three perpendiculars.
  • Applies the relationships between lines and planes, distances, and angles in space to describe real-world objects.
  • Solves problems involving finding distances and angles in space, including those with practical applications.

This course builds strong geometric fundamentals and analytical skills by integrating theoretical knowledge with practical problem-solving. Students will explore geometry through a logical, three-dimensional approach, enhancing both academic performance and mathematical thinking.

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