NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5

NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5

NCERT Solutions for Class 9 Maths Chapter 7 Triangles:

  • Triangles
  • Introduction
  • Congruence Of Triangles
  • Criteria For Congruence Of Triangles
  • Some Properties Of A Triangle
  • Some More Criteria For Congruence Of Triangles
  • Inequalities In A Triangle
  • Summary

Formulae Handbook for Class 9 Maths and Science Educational Loans in India

NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5

Question 1.
ABC is a triangle. Locate a point in the interior of ∆ ABC which is equidistant from all the vertices of ∆ ABC.
Solution:
Suppose OM and ON be the perpendicular bisectors of sides BC and AC of ∆ ABC.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 q1
So, O is equidistant from two endpoints 0 and C of line segment BC as O lies on the perpendicular bisector of BC. Similarly, O is equidistant from C and A Hence, O be an orthocentre of ∆ABC.

Question 2.
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
Solution:
Suppose BN and CM be the bisectors of ∠ ABC and ∠ ACB, respectively intersect AC and AB at N and M, respectively.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 q2
Since, O lies on the bisector BN of ∠ ABC, so O will be equidistant from BA and BC. Again, O lies on the bisector CM of ∠ ACB.
So, O will be equidistant from CA and BC. Thus, O will be equidistant from AB, BC and CA Hence, O be a circumcentre of ∆ABC.

Question 3.
In a huge park, people are concentrated at three points (see figure)
A: where these 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 exist.
Where should an ice-cream parlor be set? up so that maximum number of persons can approach it?
[Hint The parlour should be equidistant from A, B and C.]
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 q3
Solution:
The ice-cream parlor should be equidistant from A B and C for which the point of intersection of perpendicular bisectors of AB, BC, and CA should be situated.
So, O is the required point which is equidistant from A B and C.

More Resources for CBSE Class 9

Question 4.
Complete the hexagonal and star shaped Rangolies [see Fig. (i) and (ii)] 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?
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 q4
Solution:
We first divide the hexagon into six equilateral triangles of side 5cm as follow.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 q4.1
We take one triangle from six equilateral triangles as shown above and make as many equilateral triangles of one side 1 cm as shown in the figure.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 q4.2
The number of equilateral triangles of side 1 cm = 1 + 3 + 5 + 7 + 9 = 25
So, the total number of triangles in the hexagon = 6x 25 = 150
To find the number of triangles in the Fig. (ii), we adopt the same procedure.
So, the number of triangles in the Fig. (ii) = 12 x 25 = 30Q Hence, Fig. (ii) has more triangles.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles (त्रिभुज) (Hindi Medium) Ex 7.5

9 Maths Chapter 7 Triangles Optional Exercise 7.5 in English medium
9 Maths Chapter 7 Optional Exercise 7.5 in Hindi medium
Class 9 Maths chap. 7 Triangles Exercise 7.5 in English medium
Class 9 Maths chap. 7 Triangles Exercise 7.5 in English medium sols for up board, gujrat board and cbse
Class 9 Maths chap. 7 Triangles Exercise 7.5 in English medium solutions for all boards

NCERT Solutions for Class 9 Maths

  1. Chapter 1 Number systems
  2. Chapter 2 Polynomials
  3. Chapter 3 Coordinate Geometry
  4. Chapter 4 Linear Equations in Two Variables
  5. Chapter 5 Introduction to Euclid Geometry
  6. Chapter 6 Lines and Angles
  7. Chapter 7 Triangles
  8. Chapter 8 Quadrilaterals
  9. Chapter 9 Areas of Parallelograms and Triangles
  10. Chapter 10 Circles
  11. Chapter 11 Constructions
  12. Chapter 12 Heron’s Formula
  13. Chapter 13 Surface Areas and Volumes
  14. Chapter 14 Statistics
  15. Chapter 15 Probability
  16. Class 9 Maths (Download PDF)