NCERT Solutions for Class 9 Maths Chapter 7 - Exercise

Exercise 7.5

1. ABC is a triangle. Locate a point in the interior of ΔABC which is equidistant from all the vertices of ΔABC.

Ans: The circumcentre of a triangle is always equidistant from all of its   vertices.

The circumcentre is the point where the perpendicular bisectors of all the triangle's sides meet.

By sketching the perpendicular bisectors of the triangle's sides AB, BC, and CA, we may determine the circumcentre in$\Delta ABC$. The intersection of these bisectors is marked by the letter O. As a result, O is the point that is equidistant from all of $\Delta ABC$'s vertices.

2. In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Ans: The incentre of a triangle is the point that is equidistant from all the triangle's sides. The intersection point of the angle bisectors of a triangle's interior angles is the centre of the triangle.

By drawing the angle bisectors of the interior angles of this triangle in $\Delta ABC$, we may get the incentive of this triangle. It is the point at which these angle bisectors cross each other. As a result, it is the point that is equidistant from all of $\Delta ABC$'s sides.

3. In a huge park people are concentrated at three points

A. where there are different slides and swings for children, 

B. near which a man-made lake is situated, 

C. which is near to a large parking and exit. 

Where should an ice-cream parlour be set up so that the maximum number of persons can approach it? 

(Hint: The parlor should be equidistant from A, B and C)

Ans: If the ice cream parlour is equidistant from A, B, and C, the maximum number of people can approach it. A, B, and C now form a triangle. The circumcentre is the only point in a triangle that is equidistant from its vertices. As a result, the ice cream parlour should be located near ΔABC's circumcenter O.

The maximum number of people can approach it in this case.

By drawing perpendicular bisectors of the sides of this triangle, we can find the circumcentre O.

4. Complete the hexagonal and star shaped Rangolies by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

Ans: We can see that the hexagonal shaped rangoli has a total of 6 equilateral triangles of side 5 cm in it.

The star-shaped rangoli also has 6 equilateral triangles of side 5cm and a hexagon in the middle.

Therefore, star-shaped rangoli will be filled with more equilateral triangles of side 1 cm in it.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles

Opting for the NCERT solutions for Ex 7.5 Class 9 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 7.5 Class 9 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 9 students who are thorough with all the concepts from the Subject Triangles textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 9 Maths Chapter 7 Exercise 7.5 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 9 Maths Chapter 7 Exercise 7.5, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.

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