1. Properties of Triangles

Sections

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1. 1

   Classification Of Triangles

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   Triangles can be classified based on the lengths of their sides and the...

2. 1.1

   By Sides

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   This section classifies triangles based on their sides and angles.

3. 1.2

   By Angles

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   This section discusses the classification of triangles based on their...

4. 2

   Triangle Inequality Theorem

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   The Triangle Inequality Theorem states that for any triangle, the sum of the...

5. 3

   Angles Of A Triangle

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   The section focuses on the fundamental properties of angles within a...

6. 3.1

   Sum Of Angles

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   The section covers the fundamental property of triangles where the sum of...

7. 3.2

   Exterior Angle Theorem

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   The Exterior Angle Theorem states that an exterior angle of a triangle is...

8. 4

   Congruence (≅)

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   Congruence in triangles refers to the condition where two triangles are...

9. 4.1

   Key Criteria

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   This section covers the classification of triangles, including side and...

10. 4.2

    Applications

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    This section explores various applications of triangular properties in...

11. 5

    Similarity (∼)

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    This section discusses triangle similarity, highlighting the relationships...

12. 5.1

    Criteria

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    This section covers the classification, properties, and theorems related to...

13. 5.2

    Properties

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    This section covers the properties of triangles, including classifications,...

14. 6

    Special Centers Of A Triangle

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    This section explores the special centers of a triangle, including the...

15. 6.1

    Centroid (G)

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    The centroid of a triangle, denoted as G, is the point where the three...

16. 6.2

    Incenter (I)

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    The incenter of a triangle is the point where the angle bisectors intersect,...

17. 6.3

    Circumcenter (O)

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    The circumcenter is the point where the perpendicular bisectors of a...

18. 6.4

    Orthocenter (H)

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    The orthocenter (H) of a triangle is the intersection point of its...

19. 7

    Pythagorean Theorem & Its Converse

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    The Pythagorean Theorem establishes the relationship between the sides of a...

20. 8

    Trigonometry In Right Triangles

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    This section covers trigonometric ratios for right triangles, including...

21. 8.1

    Definitions

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    This section introduces key definitions and properties related to triangles,...

22. 8.2

    Basic Identities

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    This section introduces fundamental trigonometric identities, allowing...

23. 8.3

    Worked Example

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    This worked example illustrates how to apply trigonometric ratios in a right...

24. 9

    Area Of A Triangle

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    The section discusses various methods to calculate the area of a triangle...

25. 9.1

    Basic Formula

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    This section introduces the basic formulas for calculating the area of a...

26. 9.2

    Trigonometric Formula

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    This section introduces the trigonometric formula for calculating the area...

27. 9.3

    Heron’s Formula

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    Heron's formula allows for the calculation of the area of a triangle when...

28. 9.4

    Example (Heron)

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29. 10

    Law Of Sines & Law Of Cosines

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    The Law of Sines and Law of Cosines are crucial for solving non-right...

30. 10.1

    Law Of Sines

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    The Law of Sines establishes a relationship between the angles and sides of...

31. 10.2

    Law Of Cosines

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    The Law of Cosines relates the lengths of the sides of a triangle to the...

32. 10.3

    Useful Applications

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    This section discusses the practical applications of the Law of Sines and...

33. 10.4

    Detailed Worked Examples

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    This section presents detailed worked examples utilizing the Law of Sines...

34. 11

    Summary

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    The section summarizes key properties of triangles, including...

35. 12

    Final Thoughts

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    Mastering the properties of triangles is crucial for advancing in geometry...