NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5
NCERT Solutions for Class
9 Maths Chapter 7 Triangles Ex 7.5 are the part of NCERT Solutions for Class 9 Maths.
Here you can find the NCERT Solutions for Chapter 7 Triangles Ex 7.5.
- NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1
- NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.2
- NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.3
- NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.4
- NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5
Ex 7.5 Class 9 Maths Question 1.
ABC is a triangle. Locate a point
in the interior of ΔABC which is equidistant from all the vertices of ΔABC.
Solution:
∴ O is equidistant from two ends B and C of the line segment BC as O lies on the perpendicular bisector of BC.
Similarly, O is equidistant from C and A of the line segment AC as O lies on the perpendicular bisector of AC.
Thus,
the point of intersection O of the perpendicular bisectors of sides BC, CA and
AB is the required point which is equidistant from all the vertices of ΔABC.
Ex 7.5 Class 9 Maths Question 2.
In a triangle locate a point in its interior which
is equidistant from all the sides of the triangle.
Solution:
Let BE and CF be the bisectors of ∠ABC and ∠ACB respectively
intersecting AC and AB at E and F respectively.
Since O lies on BE, the bisector of ∠ABC, hence O will be equidistant from AB and BC.
Again, O lies on CF, the bisector of ∠ACB. Hence, O will be equidistant from BC and AC.
Thus, O will be equidistant from AB, BC and CA.
Ex 7.5 Class 9 Maths Question 3.
In a huge park, people are concentrated at three
points (see figure)
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 parlor be set up so that
maximum number of persons can approach it?
[Hint: The parlor should be equidistant from A, B and C.]
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.
Ex 7.5 Class 9 Maths 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?
Solution:
We first divide the hexagon into
six equilateral triangles of side 5 cm as given below:
So, the total number of triangles in the hexagon = 6 × 25 = 150.
To find the number of triangles in Fig. (ii), we follow the same procedure.
So, the number of triangles in Fig. (ii) = 12 × 25 = 300
Hence,
Fig. (ii) has more triangles.
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