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📘 Class 9 Maths Chapter 7 – Triangles | Full Chapter Summary

In this chapter, "Triangles", we study the properties of triangles, their congruence criteria, and inequalities related to them. This chapter is very important for developing reasoning skills and is the base for higher topics like quadrilaterals, circles, and similarity.


🔹 1. Basic Definitions

Triangle → A closed figure with three sides, three angles, and three vertices.

Scalene Triangle → All sides unequal.

Isosceles Triangle → Two sides equal.

Equilateral Triangle → All sides and all angles equal (each angle = 60°).

Right Triangle → One angle = 90°.


🔹 2. Angle Sum Property

The sum of all interior angles of a triangle is always 180°.


🔹 3. Congruence of Triangles

Two triangles are congruent if they are exactly equal in shape and size.

Criteria of Congruence:

✅ SSS (Side-Side-Side): All three sides equal.

✅ SAS (Side-Angle-Side): Two sides and included angle equal.

✅ ASA (Angle-Side-Angle): Two angles and included side equal.

✅ AAS (Angle-Angle-Side): Two angles and a non-included side equal.

✅ RHS (Right angle-Hypotenuse-Side): For right triangles, hypotenuse and one side equal.


🔹 4. Properties of Triangles

Angles opposite to equal sides are equal (Isosceles Triangle Property).

Converse: Sides opposite to equal angles are equal.


🔹 5. Inequalities in a Triangle

The sum of any two sides of a triangle is greater than the third side.

The side opposite to the larger angle is longer.

The angle opposite to the longer side is larger.


🔹 6. Mid-Point Theorem (Optional)

The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.


🎯 Key Learning Outcomes

Classification and properties of triangles.

Understanding and applying congruence criteria.

Solving problems using angle sum property and triangle inequalities.

Laying the foundation for quadrilaterals and similarity in higher classes.


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