United University

Geometry Grade 9. Solving triangles. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 11 hours

This interactive course introduces Grade 9 students to the exciting world of solving triangles. Through engaging activities, problem-solving tasks, and structured lessons, learners will explore key geometric principles. Topics include the Cosine Theorem, Sine Theorem, and formulas for finding the area of a triangle. The course promotes logical thinking, spatial reasoning, and the ability to apply geometry in practical scenarios.

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This interactive course introduces Grade 9 students to the exciting world of solving triangles. Through engaging activities, problem-solving tasks, and structured lessons, learners will explore key geometric principles. Topics include the Cosine Theorem, Sine Theorem, and formulas for finding the area of a triangle. The course promotes logical thinking, spatial reasoning, and the ability to apply geometry in practical scenarios.

Key Features of the Course

  • Interactive learning with geometry tasks and quizzes
  • Exploration of trigonometric theorems and triangle solving techniques
  • Development of logical reasoning and spatial thinking skills
  • Aligned with modern curriculum requirements for Grade 9 geometry

Course Modules

Module 1: Solving triangles

  • Lesson 11: Cosine Theorem
  • Practice: Solve problems and complete exercises
  • Lesson 12: Sine Theorem
  • Practice: Solve problems and complete exercises
  • Lesson 13: Solving Triangles. Applied Problems
  • Practice: Solve problems and complete exercises
  • Lesson 14: Formulas for Finding the Area of a Triangle
  • Practice: Solve problems and complete exercises
  • Independent Homework №3 (§§ 11–14)
  • Complete the test
  • Knowledge Check Tasks for §§ 11–14
  • Complete the assignments
  • Revision Exercises for Module 3
  • Section Review: § 11
  • Section Review: § 12
  • Section Review: § 13
  • Section Review: § 14
  • Summary of Module 3

Expected Learning Outcomes

  • Give examples of geometric figures and relationships listed in the module content
  • Explain what a perpendicular and its projection are, and what it means to solve a right triangle
  • Formulate:
    • Properties of a perpendicular and an oblique line
    • Definitions of sine, cosine, and tangent of an acute angle in a right triangle
    • The Pythagorean Theorem
    • Relationships between sides and angles in a right triangle
  • Identify sides of a right triangle on diagrams that correspond to sine, cosine, or tangent of a given acute angle
  • Calculate sine, cosine, and tangent values for 30°, 45°, and 60°
  • Prove the Pythagorean Theorem
  • Solve right triangles
  • Apply definitions and properties learned to solve geometric and real-life problems

This interactive course helps students master triangle-solving techniques using trigonometric theorems and area formulas. It balances theoretical knowledge with practical applications, encouraging students to solve real-world problems through geometry.

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