The Triangle and Its Properties Test

Result

The Triangle and Its Properties Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

In the given figure, $$AB \;|\;|\; DC$$, $$BO=6\; cm$$ and $$DQ= 8\; cm$$ then find the value of $$\displaystyle BP \times DO.$$

A
$$\displaystyle 48 cm^{2}$$

B
$$\displaystyle 24 cm^{2}$$

C
$$\displaystyle 56 cm^{2}$$

D
None of the above
Question 2
1 / -0

In the above figure, point $$D$$ divides $$AB$$ in the ratio $$3: 5$$. If $$BC= 4.8 \;cm$$, find the length of $$DE$$.

A
$$1.8 cm$$

B
$$2.6 cm$$

C
$$1.2 cm$$

D
$$4 cm$$
Question 3
1 / -0

In the following figure, point $$D$$ divides $$AB$$ in the ratio $$3: 5$$. Find $$\displaystyle \dfrac{AE}{EC}$$.

A
$$\dfrac{3}{5}$$

B
$$\dfrac{3}{7}$$

C
$$\dfrac{2}{5}$$

D
$$\dfrac{7}{5}$$
Question 4
1 / -0

In the given figure, $$DE\;|\;|\;BC$$, $$AE= 15\;cm$$, $$EC= 9\;cm$$, $$NC= 6\; cm$$ and $$BN=24\; cm$$. Find the length of $$ME$$ is

A
$$3.75\,cm$$

B
$$2.5\,cm$$

C
$$4\,cm$$

D
$$5.5\,cm$$
Question 5
1 / -0

Which of the following best describes the given triangle.

A
Equilateral obtuse triangle

B
Isosceles right triangle

C
Isosceles obtuse triangle

D
Isosceles acute triangle.

Solution

Let the third angle be $$x$$
It is known that sum of interior angles of a triangle is $$180^o$$
Thus, $$x+{ 36 }^{ \circ }+{ 36 }^{ \circ }={ 180 }^{ \circ }$$
$$\Rightarrow x={ 108 }^{ \circ }$$
Now two of angles of the triangle are equal and one angle is greater than $${ 90 }^{ \circ }$$
So the given triangle is an isosceles obtuse triangle.
Question 6
1 / -0

If $$4$$ cm and $$3$$ cm are the lengths of two sides of a triangle then the length of the third side may be_____.

A
$$11$$ cm

B
$$3$$ cm

C
$$5$$ cm

D
$$12$$ cm

Solution

In a triangle, sum of two sides $$ > $$ third side.

So, if two sides are $$ 4 cm $$ and $$ 7 cm $$, then considering the given options,

A. $$ 11 cm $$

$$ 4 + 7 \ngtr 11 $$

Hence, this is not the correct option.

B. $$ 6 cm $$
We see that
$$ 4 + 7 > 6 $$
$$ 4 + 6 > 7 $$
$$ 7 + 6 > 4 $$
Hence, $$ 6 cm $$ is the correct option.
Question 7
1 / -0

An exterior angle of a triangle is less than either of its interior opposite angles.

A
True

B
False

C
Ambiguous

D
Data Insufficient

Solution

In any triangle, if one of the sides is produced, then the exterior angle is equal to the sum of the opposite two interior angles which means the exterior angle will be greater than either of the interior opposite angles.
Question 8
1 / -0

In $$\Delta ABC$$, if $$\angle A = 50^0$$ and $$\angle B = 60^0$$, then the shortest and largest sides of the triangle, respectively are:

A
$$AC$$ and $$AB$$

B
$$BC$$ and $$AB$$

C
$$AC$$ and $$BC$$

D
$$BC$$ and $$AC$$

Solution

We have,
$$\angle A = 50$$ and $$\angle B = 60$$
$$\therefore \angle A + \angle B + \angle C = 180$$ $$[$$ Angle sum property of a $$\Delta$$ $$]$$
$$\Rightarrow 50 + 60 + \angle C = 180$$
$$\Rightarrow 110 + \angle C = 180$$
$$\Rightarrow \angle C = 180 - 110$$
$$\Rightarrow \angle C = 70$$
Since $$\angle A$$ and $$\angle C$$ are the smallest and largest angles respectively, therefore corresponding sides $$BC$$ and $$AB$$ are the smallest and largest sides of the triangle respectively.
Hence, option $$B$$ is the correct answer.
Question 9
1 / -0

If the angles of a triangle are in the ratio $$2:3:4$$, find the three angles.

A
$$80^o, 120^o, 160^o$$

B
$$20^o, 30^o, 40^o$$

C
$$40^o, 60^o, 80^o$$

D
None of these

Solution

The angles of a triangle are in the ratio $$2:3:4 $$.
Let $$x:y:z=2:3:4$$.
Then, $$x=2t, y=3t$$ and $$z=4t$$.

We know, by angle sum property, the sum of all angles of a triangles is $$ 180^0$$.
$$\implies$$ $$ 2t + 3t + 4t = 180^o $$
$$\implies$$ $$ 9t = 180^o$$
$$\implies$$ $$ t = 20^o $$.

Therefore, $$ x= 2\times 20^o= 40^o; y= 3\times 20^o= 60^o; z = 4\times 20^o= 80^o $$.

Hence, option $$C$$ is correct.
Question 10
1 / -0

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is:

A
Obtuse angle triangle

B
Acute angle triangle

C
Right angle triangle

D
None of these

Solution

$$\textbf{Step-1: Apply properties of sum of angles of triangle to find it's one angle}$$
$$\text{Let the angles of a triabgle be}$$ $$\alpha ,\beta ,\gamma $$
$$\text{Given}$$ $$\alpha +\beta =\gamma $$
$$\text{We now that in a sum of triangles sum of angles is}$$ $${ 180 }^{ \circ }$$
$$\text{So,}$$$$ \alpha +\beta +\gamma ={ 180 }^{ \circ }$$
$$\Rightarrow 2\gamma ={ 180 }^{ \circ }$$
$$\Rightarrow \gamma ={ 90 }^{ \circ }$$
$$\text{So, it is a right angled triangle.}$$
$$\textbf{Hence option C is correct}$$