The document Value Based Questions- Triangles Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.

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**Question 1. In a group-discussion on “Save Water” five students Shagun, Preeti, Deepak, Nitin and Piyush are possitioned 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, **Δ**ABC is an equilateral triangle.**

**(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.

∵ 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

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 work places are at A and C respectively, such that A, B and C form a triangle. BD, the bisector of ∠ABC, meets AC at 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 work places: (i) Find the distance between ‘A’ and ‘C’.**

**(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 Δ^{s}ABD and CBD,

∴ AB = CB and AD = CD

or 3y + 1 = 5x - 2

⇒ 3y - 5x = ∠3 and y + 1 = x + 2

⇒ y - x = 1

Solving 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.

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