Triangles is a core and high-weightage chapter in Class 9 Mathematics that introduces students to congruence, triangle properties, and geometric proofs. This chapter covers important topics such as congruence of triangles (SSS, SAS, ASA, RHS), properties of triangles, inequalities in a triangle, and mid-point theorem, which are frequently asked in school examinations.
NCERT Solutions for Class 9 Maths Chapter 7 – Triangles are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear diagrams and logical reasoning, helping students understand proofs confidently and score well in Class 9 exams.
Question 1
In a huge park, people are concentrated at three different points as shown in the figure:
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Point A: Where slides and swings for children are present
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Point B: Near a man-made lake
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Point C: Near a large parking area and exit
Where should an ice-cream parlour be set up so that the maximum number of people can reach it easily?
Answer
The ice-cream parlour should be set up at a point that is equidistant from all three points A, B, and C, so that people from each location can reach it easily.
If we join the three points A, B, and C, we form a triangle ABC.
The point which is at an equal distance from all three vertices of a triangle is called the circumcentre of the triangle.
The circumcentre is obtained by drawing the perpendicular bisectors of the sides of the triangle.
The point where these perpendicular bisectors intersect is the circumcentre.
Therefore, the ice-cream parlour should be set up at the circumcentre of triangle ABC.
At this point, people from all three locations can approach the parlour with minimum distance, ensuring maximum accessibility.
FAQs: Class 9 Maths Chapter 7 – Triangles
Q1. Is Triangles an important chapter for Class 9 exams?
Yes, it is a high-weightage geometry chapter with many proof-based questions.
Q2. Which topics are most important in this chapter?
Congruence of triangles, triangle inequalities, and mid-point theorem.
Q3. Are proof-based questions asked from this chapter?
Yes, theorem and proof-based questions are very common.
Q4. Is this chapter important for Class 10 Maths?
Yes, it forms the base for similarity of triangles and trigonometry.
Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with clear diagrams and logic.