Triangle Inequality 2

Q.

Give $3$ real-life examples of perpendicular lines.

Q.

X lies in the interior of $\delta ABC$. If $\angle BAC$= 70${}^{\circ }$ and $\angle BAX$ = 42${}^{\circ }$ then $\angle XAC$ =?

1. 28°

2. 29°

3. 27°

4. 30°

Q. Question 3
$\Delta ABC$, if AB =AC and $\angle B={50}^{\circ }$ then $\angle C$ is equal to
(A) ${40}^{\circ }$
(B) ${50}^{\circ }$
(C) ${80}^{\circ }$
(D) ${130}^{\circ }$

Q. ABC is an equilateral triangle of side length 20 cm. The minimum distance of vertex A from its opposite side is _____.

1. $5\sqrt{3}$
2. $10\sqrt{3}$
3. $8\sqrt{3}$
4. $4\sqrt{3}$

Q.

The sum of two sides of a triangle is greater than or equal to the third side. State whether the statement is true or false.

1. True
2. False

Q.

In the given figure, the shortest distance of point A from line $l$ is .

1. AB
2. AC
3. AD
4. AE

Q. The side length of a $\Delta$ ABC are 4, 11 and $x$. Which of the following is a possible value of $x$?

1. 12
2. 15
3. 17
4. 7

Q. 4, 7 and a are the measure of sides of a triangle. Find the range of values of a.

1. $3<s<11$
2. $3<s<8$
3. $3\le s<7$
4. $3<s\le 7$

Q. ABC is a triangle such that $AB=10cm$ and $AC=3cm$. Then which of the following is true about side BC?

1. BC < 7 cm
2. BC = 6 cm
3. BC > 13 cm
4. BC < 13 cm

Q. The side length of a non-degenerate $\Delta$ ABC are 4, 11 and x. Which of the following is a possible value of x?

1. 17
2. 7
3. 12
4. 15

Q.

The lengths of two sides of a triangle are $11cm$ and $19cm$. Identify the range of possible lengths for the third side.

1. $12\mathrm{cm}<\mathrm{x}<30\mathrm{cm}$

2. $8\mathrm{cm}<\mathrm{x}<30\mathrm{cm}$

3. $8\mathrm{cm}<\mathrm{x}<31\mathrm{cm}$

4. $11\mathrm{cm}<\mathrm{x}<19\mathrm{cm}$

Q. ABC is a triangle such that $AB=15cm$ and $AC=5cm$. The side BC lies between and .

1. 10
2. 20
3. 8
4. 12

Q. ABC is an equilateral triangle of side length 10 cm. The minimum distance of vertex A from its opposite side is.

1. $4\sqrt{3}$
2. $3\sqrt{3}$
3. $3\sqrt{3}$
4. $5\sqrt{3}$

Q.

In a triangle, the greater side is opposite to the greater angle.

1. True
2. False

Q. If the minimum distance from its opposite side of an equilateral triangle is $4\sqrt{3}$ cm, then determine the side length of the triangle.

Q. In $\Delta ABC$, if ∠A = 45° and ∠B = 65°, then the longest side of the triangle is _______.

1. AB
2. CA
3. None of the above
4. BC

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

1. greater than
2. equal to
3. less than

Q. Sum of lengths of any two sides of a triangle is always less than the length of the third side.

1. True
2. False

Q. In $\Delta ABC$, if ∠A = 45° and ∠B = 65°, then the longest side of the triangle is .

1. AB
2. BC
3. CA

Q.

Can we get a triangle ABC in which BC is 12cm, Angle B is ${75}^{\circ }$ and AB+AC=6.5cm

Answer true if it is possible else answer false.

1. True

2. False

Q. The point of intersection of the angular bisectors of a triangle is called its circumcentre.

1. False
2. True

Q.

In $∆\mathrm{ABC}$, if $\angle B=\angle C=45°$, which of the following is the longest side?

1. $AB$

2. $AC$

3. $BC$

4. None of these

Q.

In triangle ABC, D is a point on BC. If AB > BD and AC > DC then, AB + AC _____________________

1. < BC

2. = BC

3. >BC

4. > 2BC

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

1. BC < $13cm$.
2. BC < $7cm$.
3. BC > $13cm$.
4. BC = $13cm$.

Q. In $\Delta ABC$, if ∠A = 45°, ∠B = 65° and ∠C = 70°, then AB is the longest side of the triangle.

1. True
2. False

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

1. $=7$
2. $>7$
3. $<7$
4. None of these

Q. In $\Delta ABC,\angle C={60}^o$ and $\angle C>\angle B$.
Which is the longest side of the triangle?

Q.

Is it possible to draw a triangle with sides $5\mathrm{cm},6\mathrm{cm}\&13\mathrm{cm}$? Justify your answer.

Q. 6cm, 7cm and 9cm can represent sides of a triangle.

1. True
2. False

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

1. BC < 13 cm
2. BC < 7 cm
3. BC > 13 cm
4. BC = 13 cm