Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Value-Based Questions: Triangles

Class 9 Maths Chapter 6 Question Answers - Triangles

Question 1. In a group discussion on “Save Water” five students Shagun, Preeti, Deepak, Nitin and Piyush are positioned at A, B, C, X and Y respectively as shown in the following figure such that AB = AX = BX and AC = AY and CY. Also, ΔABC is an equilateral triangle.

Class 9 Maths Chapter 6 Question Answers - Triangles

(i) Show that CX = BY. 

(ii) Which mathematical concept is used in the above problem?

(iii) By arranging a group discussion on ‘save-water’, which values are depicted by the school?
 Solution. 
(i) Join BY and CX.

Class 9 Maths Chapter 6 Question Answers - Triangles

∵ ΔABC is an equilateral Δ
∴ AB = BC = AC                     ..... (1)
But AB = AX = BX                     ..... (2)
Also AC = AY = CY                     ..... (3)

∴ From (1), (2) and (3), we have:
BX = CY ..... (4)
Since, AB = AX = BX                    [Given]
∴ ΔABX is an equilateral Δ
⇒ ∠ABX = 60° Similarly ∠ACY = 60°
Also ∠ABC = ∠ACB = 60

Class 9 Maths Chapter 6 Question Answers - Triangles

Now, In ΔCBX and ΔBCY, we have BX = CY                    [from 4]
∠CBX = ∠BCY                     [Proved above]
BC = BC                    [Common]
∴ ΔCBX ≌ΔBCY
⇒ CX = BY
(ii) Triangles             [Geometry].
(iii) Inculcating discussion ability and developing an attitude of saving natural resources.

 

Question 2. Rajat and Shankar live together at B. Their workplaces are at A and C respectively, such that A, B and C form a triangle. BD, the bisector of ∠ABC, meets AC at a right angle. Various distances are expressed in terms of x and y as shown in the following figure.
They use bicycles instead of cars to go to their workplaces:
(i) Find the distance between ‘A’ and ‘C’.

Class 9 Maths Chapter 6 Question Answers - Triangles

(ii) Which mathematical concept is used in the above problem?

(iii) By using bicycles instead of cars, which values are depicted by Rajat and Shankar?
 Solution. 
(i) Since, BD is perpendicular to AC
∴ ∠3 = ∠4 = each 90°                     ..... (1)

Also, BD is bisector of ∠ABC,
∴ ∠1 = ∠2
Now, in ΔsABD and CBD,

Class 9 Maths Chapter 6 Question Answers - Triangles

∴ AB = CB and AD = CD
or 3y + 1 = 5x - 2
⇒ 3y - 5x = ∠3 and y + 1 = x + 2
⇒ y - x = 1

Solving  Class 9 Maths Chapter 6 Question Answers - Triangles               we get x = 3, y = 4
Now distance between A and C  = AD + DC
=[y + 1] km + [x + 2] km
= [4 + 1] km + [3 + 2] km
= 5 km + 5 km = 10 km

(ii) Triangles                    [Geometry].

(iii) Following value factors are depicted:
(a) Environment protection as bicycles are pollution-free.
(b) Physical exercise for good health.
(c) Saving energy as bicycles do not consume petrol.

The document Class 9 Maths Chapter 6 Question Answers - Triangles is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Class 9 Maths Chapter 6 Question Answers - Triangles

1. What are the different types of triangles?
Ans. There are three types of triangles based on their sides: scalene, isosceles, and equilateral. A scalene triangle has no equal sides, an isosceles triangle has two equal sides, and an equilateral triangle has all three sides equal.
2. How can I determine the type of triangle by its angles?
Ans. Triangles can be classified based on their angles as well. An acute triangle has all three angles less than 90 degrees, a right triangle has one angle equal to 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.
3. What is the sum of the angles in a triangle?
Ans. The sum of the three angles in any triangle is always 180 degrees. This property is known as the angle sum property of triangles.
4. How can I find the area of a triangle?
Ans. The area of a triangle can be calculated using the formula: Area = 1/2 * base * height. The base and height are perpendicular to each other and can be measured using the appropriate units.
5. Can a triangle have two right angles?
Ans. No, a triangle cannot have two right angles. The sum of the angles in a triangle is always 180 degrees, and if two angles are right angles (90 degrees each), then the third angle would be 0 degrees, which is not possible.
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