Geometry Grade 8. Solving right triangles. Collection 1

Embark on an exciting journey through Geometry! Our "Geometry Grade 8. Solving right triangles. Collection 1" course offers a dynamic learning experience that delves into the fascinating world of right triangles. Students will explore key concepts such as the Pythagorean theorem, perpendiculars, and the relationships between the sides and angles of right triangles through interactive lessons and engaging activities.

Why choose our course:

• Interactive quizzes and tests: Test your knowledge and reinforce learning with engaging and challenging quizzes.
• Expertly crafted content: Developed by experienced educators to ensure high-quality and effective learning.
• Real-life applications: Learn how geometric principles apply to real-world scenarios and various fields of study.

Course Module

Module 1: Solving right triangles.

• §18. Pythagorean Theorem
• §18. Pythagorean Theorem (Part 1)
• §18. Pythagorean Theorem (Part 2)
• §18. Pythagorean Theorem (Part 3)
• §19. Perpendiculars and Inclines, their properties
• §19. Perpendiculars and Inclines, their properties (Part 1)
• §19. Perpendiculars and Inclines, their properties (Part 2)
• §20. Sine, Cosine, and Tangent of an Acute Angle in a Right Triangle. Relationships between the sides and angles of a right triangle
• §20. Sine, Cosine, and Tangent of an Acute Angle in a Right Triangle. Relationships between the sides and angles of a right triangle (Part 1)
• §20. Sine, Cosine, and Tangent of an Acute Angle in a Right Triangle. Relationships between the sides and angles of a right triangle (Part 2)
• §20. Sine, Cosine, and Tangent of an Acute Angle in a Right Triangle. Relationships between the sides and angles of a right triangle (Part 3)
• §21. Solving Right Triangles
• §21. Solving Right Triangles (Part 1)
• §21. Solving Right Triangles (Part 2)
• Independent Homework №4 (Sections 18-21)
• Knowledge Check Tasks for Sections 18-21
• Review Exercises for Section 3
• To §18
• To §19
• To §20
• To §21
• Key Points of Section 3

Expected Learning Outcomes

• Provides examples of geometric figures and relationships as described in the course content.
• Explains the concept of an incline and its projection; defines what it means to "solve a right triangle".
• Formulates:
  • The properties of perpendiculars and inclines.
  • The definition of sine, cosine, and tangent of an acute angle in a right triangle.
  • The Pythagorean theorem.
  • The relationships between the sides and angles of a right triangle.
• Identifies on diagrams the sides of a right triangle whose ratio corresponds to the sine, cosine, and tangent of the given acute angle.
• Calculates the values of sine, cosine, and tangent for the angles 30°, 45°, and 60°.
• Proves the Pythagorean theorem.
• Solves right triangles.
• Applies the definitions and properties learned to solve problems, including real-life scenarios.

By the end of this course, students will have a solid understanding of right triangles, enabling them to confidently apply geometric principles to solve more complex problems in geometry and beyond.