NCERT Solutions for Class 9 Maths Chapter 7 Triangles Exercise 7.3

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NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Ex 7.3) Exercise 7.3

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Students will study in detail triangles and their various properties in NCERT solutions for class 9 maths chapter 7 exercise 7.3. The chapter introduces the definition of a triangle, congruence of triangles, inequalities in a triangle, rules of congruence, and more. The chapter explains some rules or criteria for the congruence of triangles. It covers Side- Angle- Side Congruence Rule, Angle- Side- Side Congruence Rule, and Angle- Angle- Side Congruence Rule. Apart from it, other properties of an isosceles triangle, theorems related to triangles, and more concepts are explained in detail in ch 7 Maths NCERT Solutions Class 9 ex 7.3. Students can also avail of NCERT Solutions for Class 9 Science from our website.

Chapter 7-Triangles part-1
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FAQ (Frequently Asked Questions)

1. How to show AB bisects PQ if AB is an altitude of an isosceles triangle APQ in which AP = AQ?

In the question, it’s given that AB is an altitude and AP = AQ. Now, in a triangle, APB and AQB, angle ABP = 90o and ABQ = 90o. As AP = AQ and AB is the common arm in the triangle APB and AQB, then apply the RHS congruence rule. The rule states that two triangles are said to be congruent if the hypotenuse and one side of a triangle are equal to another triangle’s hypotenuse and its one side. Hence, both the triangles APB and AQB are equal. Now, by applying the CPCT rule, PB is equal to QB. Hence, AB bisects PQ.

2. How to prove that the ABC is an isosceles triangle if BE and CF are two altitudes equal to each other?

Given that BE and CF are two altitudes of an isosceles triangle that are equal to each other. In the triangle BEC and CFB, angle BEC is equal to 90o and CFB is equal to 90o. Also, BC = CB as it is a common side. Similarly, BE and CF are equal. By applying the RHS Congruence Rule, triangle BEC and CFB are equal to each other. Additionally, by CPCT rule, C = B. It means that sides opposite to the equal angles are equal always. Hence, AB = AC. It shows, that side AB and BC of the triangle ABC form an isosceles triangle.