10th Class Mathematics Chapter – 6: TRIANGLES – PDF Free Download

At Ramsetu, we aim to provide educational resources that make learning engaging and comprehensive. Chapter 6, “TRIANGLES,” from the 10th Class Mathematics textbook, covers fundamental concepts related to triangles, their properties, and theorems. This chapter provides students with a thorough understanding of different types of triangles, congruence, similarity, and their applications in geometry.

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Chapter Insights:

• Summary of “TRIANGLES.”
• Explanation of key concepts and properties.
• Detailed examples and exercises.
• Practical applications and relevance of triangles in everyday life.

Key Concepts and Definitions:

• Triangle: A polygon with three edges and three vertices.
• Types of Triangles: Classification based on sides and angles.
• Congruence of Triangles: Criteria for two triangles to be congruent.
• Similarity of Triangles: Criteria for two triangles to be similar.

Chapter Content:

• Summary of “TRIANGLES”:
  • Introduction to triangles and their classification.
  • Understanding the properties of triangles.
  • Important theorems related to triangles.
• Key Concepts:
  • Types of Triangles:
    • Based on sides: Equilateral, Isosceles, and Scalene.
    • Based on angles: Acute, Right, and Obtuse.
  • Congruence of Triangles:
    • Criteria: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and RHS (Right angle-Hypotenuse-Side).
  • Similarity of Triangles:
    • Criteria: AA (Angle-Angle), SSS (Side-Side-Side), and SAS (Side-Angle-Side).
  • Pythagoras Theorem:
    • In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
  • Basic Proportionality Theorem (Thales’ Theorem):
    • If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
• Formulas and Properties:
  • Pythagoras Theorem: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2 (where ccc is the hypotenuse)
  • Area of a Triangle: Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21​×base×height
  • Similarity Ratio: If two triangles are similar, the ratio of their corresponding sides is equal.
• Applications:
  • Real-life applications of triangles in construction, engineering, and design.
  • Use of the Pythagorean theorem in various fields such as architecture and navigation.
  • Understanding the significance of similarity and congruence in solving geometrical problems.

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