**CBSE Class 9 Maths Lab Manual – Relations of Inequalities in Triangles**

**Objective**

To verify that a triangle is possible only if the sum of any two sides of triangle is always greater than the third side and difference of any two sides is always less than the third side.

**Prerequisite Knowledge**

- Measurement of line segments.
- Comparison of line segments.

**Materials Required**

Broom sticks or straws, scale, geometry box.

**Procedure**

- Take some sticks according to the given measurements.
- Collect three triplets of sticks as given.
**Set I**- 3cm, 5cm, 10cm

- 4cm, 4cm, 8cm

- 5cm, 4cm, 8cm

**Set II**- 3cm, 4cm, 8cm

- 4cm, 6cm, 10cm

- 4cm, 5cm, 7cm

**Set III**- 5cm, 3cm, 6cm

- 5cm, 5cm, 11cm

- 3cm, 2cm, 5cm

- Now from the above three sets, try to form a triangle and name them.

**Observation and Calculation**

**Table **

Set | Side 1 | Side 2 | Side 3 | Possibility of ∆ | Reason |

I | |||||

(i) | 3 | 5 | 10 | not possible | 3 +5 < 10 |

(ii) | 4 | 4 | 8 | not possible | 4 + 4 = 8 |

(iii) | 5 | 4 | 8 | possible | 5 + 4 > 8; 5 + 8 > 4; 4 + 8 > 5 |

II | |||||

(i) | 3 | 4 | 8 | not possible | 3 + 4 < 8 |

(ii) | 4 | 6 | 10 | not possible | 4 + 6 = 10 |

(iii) | 4 | 5 | 7 | possible | 4+5 > 7; 5 + 7 > 4; 4 + 7 > 5 |

III | |||||

(i) | 5 | 3 | 6 | possible | 5 + 3> 6; 5 + 6 > 3; 3 + 6 > 5 |

(ii) | 5 | 5 | 11 | not possible | 5 + 5 < 11 |

(iii) | 3 | 2 | 5 | not possible | 3 + 2 = 5 |

** **In each set, we observe that triangle is possible only when the sum of the two sides is greater than the third side.

**Result**

We verified that the triangle is possible only when sum of any two sides is greater than the third side.

**Learning Outcome**

We learnt that, for any three line segments, we cannot construct triangle always because for a triangle the sum of any two sides of a triplet is always greater than the third side.

**Activity Time**

- For a triplet, verify that the difference of any two sides is always less than third side in a triangle.
- Are the following triangles possible?
- Right-angled equilateral triangle.
- Obtuse equilateral triangle.
- All angles are acute angle.
- Two obtuse angles in a triangle.

**Viva Voce**

**Question 1.**

State, if the following triangles are possible:

- 7cm, 9cm, 11cm
- 10cm, 9cm, 19cm,

**Answer:**

- Yes
- No.

**Question 2.**

What are an equilateral, scalene, isosceles triangles ?

**Answer:**

Equilateral triangle → having all sides equal.

Scalene triangle → having all three sides different.

Isosceles triangle → having any two equal sides.

**Question 3.**

Is right angled equilateral triangle possible ?

**Answer:**

No.

**Question 4.**

Is right angled isosceles triangle possible ?

**Answer:**

Yes.

**Question 5.**

Is obtuse equilateral triangle possible ?

**Answer:**

No.

**Question 6.**

Will a triangle be possible with all acute angles ?

**Answer:**

Yes.

**Question 7.**

Is a triangle possible, if the area of triangle is zero ?

**Answer:**

No.

**Question 8.**

What is the angle sum property of a triangle ?

**Answer:**

In a triangle, the sum of its all three angles is 180°.

**Question 9.**

What is the relationship between the sum of two sides of a triangle ?

**Answer:**

In a triangle, sum of two sides is always greater than third side.

**Question 10.**

What is the relationship between the difference of two sides of a triangle to the third side ?

**Answer:**

In a triangle, difference of two side is always less than the third side.

**Multiple Choice Questions**

**Question 1.**

In a AABC, ∠A = 95°, ∠B = 60°, what will be the least side of ∆ABC ?

(i) AB

(ii) BC

(iii) AC

(iv) none of these

**Question 2.**

Arrange the sides of ∆PQR in ascending order of magnitude, if in ∆PQR, ∠P = 90°, ∠Q = 60°:

(i) PQ < PR < QR (ii) QR > PR > PQ

(iii) QR > PQ > PR

(iv) none of these

**Question 3.**

In the given figure, if x > y, what is the relationship between ∠PQR and ∠PRQ:

(i) ∠PQR = ∠PRQ

(ii) ∠PQR > ∠PRQ

(iii) ∠PRQ > ∠PQR

(iv) none of these

**Question 4.**

In a quadrilateral, what is the relationship between sum of four sides and sum of two diagonals :

(i) sum of four sides > sum of diagonals

(ii) sum of diagonals > four sides

(iii) sum of four sides = sum of diagonals

(iv) none of these

**Question 5.**

Which is the longest side in right angled triangle ?

(i) altitude

(ii) base

(iii) hypotenuse

(iv) none of these

**Question 6.**

If three triplets are 7, 9, 6, is the triangle possible by using these triplets ?

(i) not possible

(ii) yes

(iii) right triangle is possible

(iv) none of these

**Question 7.**

Is the obtuse right triangle possible ?

(i) no

(ii) yes

(iii) can’t say

(iv) none of these

**Question 8.**

The three values of angles are 60°, 90°, 30°. Is the triangle possible by using these angles ?

(i) right triangle

(ii) yes

(iii) no

(iv) none of these

**Question 9.**

What is the shortest distance between a point and a line ?

(i) any distance

(ii) perpendicular distance

(iii) not particular distance

(iv) none of these

**Answers**

- (i)
- (i)
- (iii)
- (i)
- (iii)
- (ii)
- (i)
- (i), (ii)
- (ii)

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