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.
Create and maintain a robust foundation in all the topics of chapter 7 class Maths. NCERT Solutions for Class 9 maths chapter 7 exercise 7.3 provided by professionals are well-written with step-by-step explanations. These solutions come in handy so that students can rapidly finish their homework and class assessments. Since the interpretation of the questions is such a vital aspect when solving Maths problems, academicians pay special attention to make these solutions student-friendly.Â
Class 9 maths exercise 7.3 educates students that a triangle is a closed figure formed by three lines intersecting. In the first section of the chapter, students will learn that if two figures possess the same shape and same size, then they are called congruent. Some of the examples include two squares of the same sides, two circles of the same radius, and two triangles whose corresponding parts are congruent. Theorems covered in class 9 maths ex 7.3 involve angles opposite to the equal sides and more.Â
Students will come across some congruence rules such as SAS, AAS, and ASA. SAS, which refers to Side- Angle- Side Congruence Rule states that if two sides and the comprised angle of one triangle are equal to the sides, and the formed angle of the other triangle, then two triangles are congruent. ASA, which refers to Angle- Side- Angle Congruence Rule, states that if two angles and the comprised side of one triangle are equal to two angles, and the formed side of the other triangle, then two triangles are congruent.
Apart from it, students will study the Side- Side- Side Congruence Rule in exercise 7.3 maths class 9. The rule states that two triangles are said to be congruent if three sides of one triangle are equal to the other triangleâ€™s sides. Right angle- Hypotenuse- Side Congruence Rule states that two triangles are said to be congruent if the hypotenuse and one side of a triangle are equal to another triangleâ€™s hypotenuse and its one side. Some of the inequalities in a triangle are also discussed in this section. Students should practice ample questions discussed in exercise 7.3 class 9 NCERT solutions for better understanding and marks.Â
Triangles being a part of the Geometry unit hold a weightage of 22 marks out of 80 marks in class 9 Maths exam.Â
NCERT solutions help students to provide a strong foundation over the concepts covered in exercise 7.3. Answering the NCERT questions, require in-depth knowledge along with a better understanding of formulae. Thus, itâ€™s preferable to check expert-written solutions following the correct approach for every question given in the exercise. Some of the benefits of considering NCERT solutions for class 9 maths chapter 7 exercise 7.3 include:
Every question and answer discussed are provided by a professional expert with an all-inclusive explanation.Â
Maths NCERT solutions class 9 chapter 7 exercise 7.3 solutions help students to select a higher-grade stream according to their interest.Â
NCERT solutions offered by Vedantu are well-prepared according to the guidelines of the CBSE board.
By practicing NCERT exercise 7.3 solutions, students can find it hassle-free to solve questions asked from the chapter Triangles in exams effortlessly.Â
The students can score a good percentage in their annual examinations after referring through these solutions.
1. How to show AB bisects PQ if AB is an altitude of an isosceles triangle APQ in which AP = AQ?
In the question, itâ€™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 triangleâ€™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.
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