CLASS 9 MATH NCERT SOLUTION FOR CHAPTER – 7 TRIANGLES EX – 7.5

Triangles

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

Solution:
Let us consider a ∆ABC.
Draw l, the perpendicular bisector of AB.
Draw m, the perpendicular bisector of BC.
Let the two perpendicular bisectors l and m meet at O.
O is the required point which is equidistant from A, B and C.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 Q1
Note: If we draw a circle with centre O and radius OB or OC, then it will pass through A, B and C. The point O is called circumcentre of the triangle.

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

Solution:
Let us consider a ∆ABC.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 Q2
Draw m, the bisector of ∠C.
Let the two bisectors l and m meet at O.
Thus, O is the required point which is equidistant from the sides of ∆ABC.
Note: If we draw OM ⊥ BC and draw a circle with O as centre and OM as radius, then the circle will touch the sides of the triangle. Point O is called incentre of the triangle.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 Q2.1

Question 3.
In a huge park, people are concentrated at three points (see figure)
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 Q3

  • 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.]

Solution:
Let us join A and B, and draw l, the perpendicular bisector of AB.
Now, join B and C, and draw m, the perpendicular bisector of BC. Let the perpendicular bisectors l and m meet at O.
The point O is the required point where the ice cream parlour be set up.
Note: If we join A and C and draw the perpendicular bisector, then it will also meet (or pass through) the point O.
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5 Q3.1

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:
It is an activity.
We require 150 equilateral triangles of side 1 cm in the Fig. (i) and 300 equilateral triangles in the Fig. (ii).
∴ The Fig. (ii) has more triangles.

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