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Chapter: Theorems in Geometry & Trigonometry

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Sections

  • 1

    Key Theorems In Geometry

    This section explores key theorems in geometry, including the Pythagorean Theorem, Triangle Sum Theorem, and others that are fundamental to geometric reasoning.

    Learning Practice

  • 1.1

    Pythagoras’ Theorem

    Pythagoras’ Theorem identifies the relationship between the sides of a right-angled triangle, crucial for various applications in geometry and real life.

    Learning Practice

  • 1.2

    The Converse Of Pythagoras' Theorem

    The Converse of Pythagoras' Theorem helps identify right-angled triangles based on the relationship between the sides.

    Learning Practice

  • 1.3

    The Triangle Sum Theorem

    The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180°.

    Learning Practice

  • 1.4

    The Exterior Angle Theorem

    The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

    Learning Practice

  • 1.5

    Isosceles Triangle Theorem

    The Isosceles Triangle Theorem states that in an isosceles triangle, the angles opposite the equal sides are equal.

    Learning Practice

  • 1.6

    Basic Proportionality Theorem (Thales’ Theorem)

    The Basic Proportionality Theorem, or Thales' Theorem, states that a line drawn parallel to one side of a triangle divides the other two sides proportionally.

    Learning Practice

  • 2

    Key Theorems In Trigonometry

    This section introduces the fundamental theorems of trigonometry related to right triangles, including important identities and definitions.

    Learning Practice

  • 2.1

    Trigonometric Ratios In A Right Triangle

    Trigonometric ratios define the relationships between the sides of a right triangle, using sine, cosine, and tangent functions.

    Learning Practice

  • 2.2

    Pythagorean Identity

    The Pythagorean identity states that for any angle θ, the sum of the squares of the sine and cosine of that angle equals one.

    Learning Practice

  • 2.3

    Complementary Angle Theorem

    The Complementary Angle Theorem states the relationships between sine, cosine, and tangent for complementary angles.

    Learning Practice

  • 2.4

    Angle Of Elevation And Depression

    This section defines the angles of elevation and depression and discusses their applications in real-life scenarios.

    Learning Practice

  • 3

    Real-World Applications

    This section outlines the practical applications of key geometric and trigonometric concepts in various fields.

    Learning Practice

  • 4

    Worked Examples

    This section provides worked examples illustrating key concepts in geometry and trigonometry, enabling students to apply theorems to real-world problems.

    Learning Practice

  • 5

    Practice Exercises

    This section presents practice exercises related to theorems in geometry and trigonometry.

    Learning Practice

  • 6

    Chapter Summary

    This chapter outlines the essential theorems in geometry and trigonometry, emphasizing their applications in problem-solving and real-world contexts.

    Learning Practice

References

10 IB g&t ch3.pdf

Class Notes

Memorization

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