Relationship between Sides of a Triangle

Q.

In Fig. T is a point on side QR of $\Delta PQR$ and S is a point such that RT = ST. Which of the following is true?

1. PQ + PR < QS

2. PQ + PR > QS

3. PQ + TR > QS

4. PQ + TR < QS

Q. Which of the following statement(s) is/are not true?

1. The sum of the lengths of two sides in a triangle is always less than the length of third side.
2. The sum of the lengths of two sides in a triangle is more than the length of third side but not always.
3. The sum of the lengths of two sides in a triangle is always more than the length of third side.
4. The differnce of the lengths of two sides in a triangle is always less than the length of third side.

Q. Which of the following sets of sides form a triangle?

1. 2 cm, 3 cm, 5 cm
2. 3 cm, 4 cm, 5 cm
3. 1 cm, 1 cm, 2 cm
4. 3 cm, 4 cm, 8 cm

Q. Which of the following triplets (in cm) can act as sides of a triangle?

1. 20, 21, 19
2. 11, 10, 22
3. 35, 96 , 61
4. 25, 2 , 22

Q.

If AM is a median of triangle ABC, then which of the following relation will always hold good?

1. AB + BC + CA = 2AM

2. AB + BC + CA $>$​ 2AM

3. AB + BC + CA $<$​ 2AM

4. AB + BC + CA = AM

Q. If D is any point on the side BC of $\Delta ABC$, then

1. AB + BC + CA = 2AD
2. AB + BC + CA > 2AD
3. AB + BC + CA < 2AD
4. AB + BC - CA > 2AD

Q. Difference of lengths of any two sides is always greater than the third side.

1. True
2. False

Q. The sum of the lengths of sides is always than/to the third side is a condition to construct a triangle.

1. two
2. lesser
3. greater
4. any two
5. equal

Q.

$\text{ABC is a triangle such that AB = 10 cm}\text{and AC = 3 cm. Which of the following}\text{statements are true?}$

1. $BC>7cm$

2. $BC=6cm$

3. $BC<13cm$

4. $BC=14cm$

Q.

The length of two sides of a triangle is 3 cm and 4 cm. Which of the following integral values can the third side take?

1. $1$

2. $4$

3. $6$

4. $7$