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 5 Triangles 5.5 1
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 5 Triangles 5.5 2
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 5 Triangles 5.5 3
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.

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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?
study rankers class 9 maths Chapter 5 Triangles 5.5 4
Solution:
We first divide the hexagon into six equilateral triangles of side 5cm as follow.
NCERT Solutions for Class 9 Maths Chapter 5 Triangles 5.5 4a
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.

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