Triangles Class 9 Notes Maths Chapter 5

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CBSE Class 9 Maths Notes Chapter 5 Triangles Pdf free download is part of Class 9 Maths Notes for Quick Revision. Here we have given NCERT Class 9 Maths Notes Chapter 5 Triangles.

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.

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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