# NCERT Class 9 Maths Chapter 7 Triangles (Latest Edition)

Gurmeet Kaur

Download the Class 9 Maths Chapter 7 - Triangles in PDF format. Students should study the chapter provided by Jagran Josh only as we present you the latest edition of the chapter which is available at the official website of NCERT. Along with the PDF of Triangles chapter, you can also access the best explained NCERT Solutions from this article. We have also provided some important questions at the end of the article for self-assessment and the board exam preparations.

About Class 9  Maths Chapter 6 Triangles

Class 9 Maths Chapter - Triangles discusses about the Congruence of triangles. It also explains some other important concepts like isosceles triangle and inequalities of sides and angles of a triangle.

Major topics discussed in the chapter are:

→ Explanation of Congruence of Triangles

→ Various Criteria for Congruence of Triangles

→ Some Properties of a Triangle

→ Isosceles triangle

→ Inequalities in a Triangle

A screenshot of the NCERT Class 9 Maths Chapter 7 is given below:

Some important points to revise from the chapter are:

• Two figures are congruent, if they are of the same shape and of the same size.

• Two circles of the same radii are congruent.

• Two squares of the same sides are congruent.

• If two triangles ABC and PQR are congruent under the correspondence A ↔ P, B ↔ Q and C ↔ R, then symbolically, it is expressed as ∆ ABC ≅ ∆ PQR.

• If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent (SAS Congruence Rule).

• If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent (ASA Congruence Rule).

• If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent (AAS Congruence Rule).

• Angles opposite to equal sides of a triangle are equal.

• Sides opposite to equal angles of a triangle are equal.

• Each angle of an equilateral triangle is of 60°.

• If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent (SSS Congruence Rule).

• If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent (RHS Congruence Rule).

• In a triangle, angle opposite to the longer side is larger (greater).

• In a triangle, side opposite to the larger (greater) angle is longer.

• Sum of any two sides of a triangle is greater than the third side.

Try some important questions given below for self-assessment:

1. In a △ABC if ∠A = 45o and ∠B = 70o then determine the shortest and largest sides of the triangle.

2. In an acute angled △ABC, S is any point on BC. Prove that AB + BC + CA > 2AS.

3. Prove that if two angles of a triangle are equal then the sides opposite to them are also equal.

4. In the following figure, ∠B =  ∠C. Show that AE > AF.

5. Q is a point on the side SR of a △PSR such that PQ = PR. Prove that PS > PQ.

Also Check:

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