United University

Geometry Grade 9. Geometric transformations. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 15 hours

This section develops a solid understanding of plane transformations and their properties. Through guided lessons, practice sets, and tests, students explore isometries (motions), symmetry, rotation, translation, and similarity, and learn to use these tools to reason about equal and similar figures and their areas.

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This section develops a solid understanding of plane transformations and their properties. Through guided lessons, practice sets, and tests, students explore isometries (motions), symmetry, rotation, translation, and similarity, and learn to use these tools to reason about equal and similar figures and their areas.

Key Features of the Course

  • Step-by-step lessons with practice tasks and tests
  • Clear treatment of motions (isometries), point/line symmetry, rotations, translations, and similarity
  • Focus on visualization, logical reasoning, and proof by transformations
  • Aligned with Grade 9 geometry curriculum standards

Course Modules

Module 5: Geometric Transformations

  • Lesson 18: Motions (Isometries) and Their Properties. Equality (Congruence) of Figures
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Lesson 19: Point Symmetry
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Lesson 20: Line (Axial) Symmetry
  • Solve problems and complete exercises
  • Lesson 21: Rotation
  • Solve problems and complete exercises
  • Lesson 22: Translation
  • Solve problems and complete exercises
  • Independent Homework №5 (§§ 18–22)
  • Take the tests
  • Knowledge-check tasks for §§ 18–22
  • Complete the tasks
  • Review Exercises for Module 5
  • For § 18 • For § 19 • For § 20 • For § 21 • For § 22
  • Key Concepts of Module 5
  • Summing Up
  • Challenging Problems (Advanced)

Problems of increased complexity

  • Section 1: Coordinate Method in the Plane
  • Section 2: Vectors in the Plane
  • Section 3: Solving Triangles
  • Section 4: Regular Polygons
  • Section 5: Geometric Transformations (this collection)
  • Appendix

Expected Learning Outcomes

  • Give examples of figures and their images under the studied transformations; identify figures with a center or an axis of symmetry; recognize congruent figures
  • Explain: motion (isometry), image of a figure under a transformation, symmetry with respect to a point/line, translation, rotation, congruence of figures
  • Formulate: the definition of congruent figures; key properties of motions; properties of point/line symmetry, translation, and rotation
  • Depict and locate on diagrams the images of given figures under various transformations
  • Justify: symmetry of two figures w.r.t. a point/line; the presence of a center/axis of symmetry; congruence via transformations
  • Apply learned definitions and properties to solve geometric problems, including proofs and construction-based tasks

This collection blends transformation theory with practice. Students build visual intuition, master proof techniques via motions and similarity, and are prepared to tackle both academic and real-world geometry challenges.

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