The Sum of Any Two Sides of a Triangle Is Greater Than the Third Side

Q. In ∆PQR , PQ =6cm, PR=8cm and P is the orthocentre. What is the length of QR ?
(A) 9cm
(B) 8cm
(C) 10cm
(D) cannot be determined

Q.

In a triangle ABC if O is any point inside the triangle then prove that AB + BC + CA < 2 (AO + BO + CO ).

Q.

If AB = 8 cm, BC = 15 cm and CA = 19 cm. State whether these sides form a triangle ΔABC.

1. Yes, they form an right angled triangle

2. Yes, they form an isosceles triangle

3. No, a triangle cannot be formed

4. Yes, they form a triangle as sum of two sides is greater than the third side

Q.

1:√2:1 are the sides of a triangle. Show that it is a right angled triangle.

Q. In a triangle ABC if inradius is equal to 2 and incircle touches the side BC, CA and AB at D, E, and F. If BD, CE, AF are three consecutive even integers, then the perimeter of the triangle is (1) 36 (2) 48 (3) 12 (4) 24

Q.

The lengths of the sides of some triangles are given, which of them is not a right angled triangle?

1. 7 cm, 24 cm, 25 cm

2. 3 cm, 4 cm, 5 cm

3. 5 cm, 8 cm, 10 cm

4. 5 cm , 12 cm, 13cm

Q.

In the figure below, if AC$>$AB and D is point on AC such that AB = AD, then the relation between BC and CD is BC$>$CD.

1. True

2. False

Q. In an isosceles triangle, the length of hypotenuse is 4 root 2. the length of each of its equal side is-

Q.

Sum of any two sides of a triangle is always __________ third side in a triangle.

1. Less than

2. Greater than

3. Equal to

4. Cannot be determined

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.

Sum of two sides of a triangle is greater than the third side.

1. True

2. False

Q.

In the given figure, PQR is a triangle and S is any point in its interior. Then which of the following option is correct?

1. $SQ+SR<PQ+PR$
2. $SQ+SR>PQ+PR$
3. $SQ+PQ>SR+PR$
4. $SQ-SR>PQ-PR$

Q. Choose the related correct pairs.

1. Sum of 2 sides
2. 2 unequal sides
3. greater than 3rd
4. Equality
5. Inequality
6. Congruency

Q. Which of the following sides can form the triangle ?

1. AB= 5 m, BC = 4 m, AC =9 m
2. AB= 5 m, BC = 4 m, AC =8 m
3. AB= 5 m, BC = 4 m, AC =14 m
4. AB= 5 m, BC = 4 m, AC = 12 m

Q.

Which of the following could represent length of sides of a triangle?

1. 3, 4, 5

2. 1, 2, 3

3. 2, 4, 6

4. All of these

Q. If x, y and z are the 3 sides of a triangle, then select the correct ones.

1. x+y > z
2. x-y > z
3. y + z > x
4. y - z > x
5. x+z > y
6. z< x+y
7. x < y+ z
8. y < x+ z

Q.

ABC is a triangle such that $AB=10$ and $AC=3$. The side BC is:

1. Equal to 7

2. Greater than 7

3. Less than 7

4. None of these