Trigonometry Lecture Notes

Introduction

• Discussed the complexity of the chapter and the aim to simplify it.
• Emphasized that the goal is to make every concept clear and enjoyable.
• Mentioned the importance of scoring full marks in mathematics.

Basics of Triangles

• A figure with three angles is called a triangle.
• Triangle sides and angles are named as ABC.
• Property of triangles: The sum of internal angles is 180 degrees.
• Naming angles with three letters for clarity, e.g., angle BAC.

Properties of Triangles

• The sum of internal angles of a triangle is 180 degrees.
• Exterior angle properties and adjacent angle properties.

Congruence of Triangles

• Definition: Figures having the same shape and size are congruent.
• Explanation through various examples.
• Two triangles are congruent if their corresponding parts (sides and angles) are equal. Shorthand: CPCT (Corresponding Parts of Congruent Triangles).
• To prove triangles congruent, we use rules like SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side).

Congruence Criteria

SSS (Side-Side-Side)

• If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

SAS (Side-Angle-Side)

• If two sides and the included angle of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.

ASA (Angle-Side-Angle)

• If two angles and the included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.

AAS (Angle-Angle-Side)

• If two angles and a non-included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.

RHS(Right-Hpotenuse-Side)

• If the hypotenuse and one side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.

Working through Examples

• Detailed explanation of problems involving congruence criteria.
• Emphasized on understanding through examples rather than rote memorization.

Isosceles Triangle Properties

• In an isosceles triangle, the angles opposite to the equal sides are equal.
• If two angles are equal, then the sides opposite to these angles are also equal.
• Proved through construction and congruence.

Working through Complex Problems

• Emphasized on problem-solving techniques involving complex geometrical proofs.
• Introduced methods for dealing with unknown angles through known properties.
• Use of perpendicular bisector and angle bisector concepts to aid in proofs.

Conclusion

• Recap of five key congruence rules: SSS, SAS, ASA, AAS, and RHS.
• Importance of understanding and practicing these rules through various problems.
• Encouragement to solve exercises from NCERT and other sources to solidify understanding.