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Triangles Class 9 Notes Maths Chapter 5

 

CBSE Class 9 Maths Notes Chapter 5 Triangles

1. Triangle: A closed figure formed by three intersecting lines is called a triangle (‘Tri’ means ‘three’). A triangle has three sides, three angles and three vertices.
Triangles Class 9 Notes Maths Chapter 5 1
e.g., In triangle ABC, denoted as ∆ABC. AB, BC, CA are the three sides, ∠A, ∠B, ∠C are the three angles and A, B, C are three vertices.

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    2. Congruence of Triangles: Two triangles are congruent if the sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.
    If ∆PQR is congruent to ∆ABC, we write ∆PQR = ∆ABC.
    Note: Congruent triangles corresponding parts are equal and we write in short ‘CPCT’ for Corresponding Parts of Congruent Triangles.

    3. Criteria for Congruence of Triangles.

    • SAS congruence rule: Two triangles are congruent if two sides and the included angle of one triangle are equal to the sides and the included angle of the other triangle.
    • ASA congruence rule: Two triangles are congruent if two angles and the included sides of one triangle are equal to two angles and the included side of another triangle.
    • AAS congruence rule: Two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal.
    • SSS congruence rule: Two triangles are congruent if three sides of one triangle are equal to the sides of the other triangle.
    • RHS congruence rule: If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangles, then the two triangles are congruent.

    4. Properties of a Triangle

    • Isosceles triangle: A triangle in which two sides are equal is called an isosceles triangle. So, ∆ABC is an isosceles triangle with AB = AC.
      Triangles Class 9 Notes Maths Chapter 5 2
    • Theorem 1: Angles opposite to equal sides of an isosceles triangle are equal.
      i.e., ∠B = ∠C
    • Theorem 2: The sides opposite to equal angles of a triangle are equal. i.e., AB = AC

    5. Inequalities in a Triangle

    • If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).
    • In any triangle, the side opposite to the larger (or greater) angle is longer (converse of (i)).
    • The sum of any two sides of a triangle is greater than the third side, i.e., AB + BC > CA.

    We hope the given CBSE Class 9 Maths Notes Chapter 5 Triangles Pdf free download will help you. If you have any query regarding NCERT Class 9 Maths Notes Chapter 5 Triangles, drop a comment below and we will get back to you at the earliest.

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