The Triangle and Its Properties Test

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The Triangle and Its Properties Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

$$ABCD$$ is a rectangle. If ABP and BCQ are equilateral triangle, $$\angle PBQ$$ = ....

A
$$65^0$$

B
$$75^0$$

C
$$60^0$$

D
$$90^0$$

Solution

$$ABCD$$ is a rectangle. So, $$\angle ABC=90^0$$
ABP and BCQ are equilateral triangle, So, $$\angle CBQ=\angle ABP = 60^0$$
So,
$$\angle PBQ=\angle ABC-\angle ABP+\angle CBQ\\=90^0-60^0+60^0\\=90^0$$
Question 2
1 / -0

Which of the following statements is correct?

A
A triangle can have two right angles.

B
All the angles of a triangle are more than 60$$^o$$

C
An exterior angle of a triangle is always greater than each of the opposite interior angles.

D
All the angles of a triangle are less than 60$$^o$$

Solution

(A), If a triangle has two right angles, the third angle will become zero angle. The statement is false.
(B) If all angles of the triangles are greater than $$60^o$$, then sum of angles in triangle will be greater than $$180^o$$. The statement is false.
(C) An exterior angle of a triangle is equal to sum of the opposite interior angles, hence it will be greater than each of the opposite interior angles. The statement is correct.
(D) If all angles of the triangles are less than $$60^o$$, then sum of angles in triangle will be less than $$180^o$$. The statement is false.
Hence option (C) is the correct answer.
Question 3
1 / -0

If two sides of an isosceles triangle are 4 cm and 10 cm then the length of the third side is__

A
4 cm

B
10 cm

C
4 cm or 10 cm

D
None of these

Solution

Two sides of an isosceles triangle are $$4$$ cm and $$10$$ cm

In an isosceles triangle two sides are equal.

Case 1:

Let the third side be $$4$$ cm.

For any triangle with sides let say $$a , b ,c$$, then

$$a+b > c$$ and

$$c+b > a$$ and

$$c+a > b$$

In this case $$4+4 = 8 < 10$$

So, the third side of $$4$$ cm will not possible.

Case 2:

Let third side be $$10$$ cm

$$10+4=14> 10$$ and

$$10+10=20>10$$

Therefore, $$10$$ cm is the third side.

Hence, the length of the third side is $$10$$ cm.
Question 4
1 / -0

The angles in a right-angled triangle other than the right angle are-

A
Right

B
Obtuse

C
Acute

D
None of these

Solution

$$\displaystyle \because $$ One of the angle is $$\displaystyle 90^{\circ}$$ and the sum of other two angles is $$\displaystyle 90^{\circ}$$ So they are acute
Question 5
1 / -0

The sides of a right triangle are $$(x-1)$$, $$x$$ and $$(x+1)$$. Find the sides of the triangle.

A
$$3, 4, 5$$

B
$$5, 5, 6$$

C
$$2, 3, 4$$

D
None of these

Solution

The sides of a triangle given are $$x-1, x$$ and $$x+1.$$
$$\because x+1>x>x-1,$$ $$\forall x>0$$
$$\implies$$ $$x+1$$ is the longest side
As it is a right angled triangle, we apply Pythagoras theorem
therefore,
$$\left ( x-1 \right )^{2}+x^{2}=\left ( x+1 \right )^{2}$$
$$\Rightarrow x^{2}-2x+1+x^{2}=x^{2}+2x+1$$
$$\Rightarrow x^{2}-4x=0$$
$$\Rightarrow x\left ( x-4 \right )=0$$
$$x=4$$ ,$$x=0$$
$$x=0$$ cannot be the side of a triangle.
One side is $$4.$$
Other two sides
$$x-1=4-1=3$$
$$x+1=4+1=5$$
$$\therefore$$ Sides of a triangle are $$3,4$$ and $$5.$$
Answer is option $$\text{A}$$
Question 6
1 / -0

If two angles of a triangle are acute angles, then the third angle:

A
is less than the sum of the two angles

B
should be an acute angle

C
is the largest angle of the triangle

D
is an angle with any measurement less than $$180^o$$
Question 7
1 / -0

Measure of $$\displaystyle x^{0}$$ in the figure is

A
$$\displaystyle 60^{0}$$

B
$$\displaystyle 70^{0}$$

C
$$\displaystyle 80^{0}$$

D
$$\displaystyle 55^{0}$$

Solution

Using exterior angle property,
$$\displaystyle x^{0} + 50^{0} =120^{0} $$
$$\displaystyle x^{0} =120 ^{0} - 50^{0}= 70^{0} $$
Question 8
1 / -0

The number of lines of symmetry in a scalene triangle is

A
0

B
1

C
2

D
3

Solution

Scalene triangle has no equal sides and no equal angles so the number of line of symmetry in a scalene triangle id Zero.
Question 9
1 / -0

Find the value of $$AC.$$

A
$$40 \ m$$

B
$$42 \ m$$

C
$$41 \ m$$

D
$$46 \ m$$

Solution

In $$\Delta ABC$$ using Pythagoras theorem,
$$AC^2 = AB^2 + BC^2 $$
$$AC =\sqrt{9^2+40^2}=\sqrt{81+1600m}=\sqrt{1681}=41 \ m$$
Question 10
1 / -0

Which of the following sets of side lengths form a triangle?

A
4 m, 3 m, 11 m

B
7 mm, 4 mm, 4 mm

C
3 cm, 1.1 cm, 5 cm

D
3 m, 4 m, 8 m

Solution

A triangle can be formed only if sum of any two sides is greater than the third side.
In option $$B$$ sum of any two sides taken at a time is greater than the third side.
$$7+4 = 11>4$$
$$4+4= 8>7$$
$$4+7= 11>4$$
In all other options, sum of first two sides is less than the third side:
A) $$4+3<11$$
C) $$3+1.1<5 $$
D) $$3+4<8$$
So option $$B$$ is correct.

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Re-Attempt Weekly Quiz Competition

The Triangle and Its Properties Test - 19

Result

The Triangle and Its Properties Test - 19

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SHARING IS CARING

Question 1

$$65^0$$

$$75^0$$

$$60^0$$

$$90^0$$

Solution

Question 2

A triangle can have two right angles.

All the angles of a triangle are more than 60$$^o$$

An exterior angle of a triangle is always greater than each of the opposite interior angles.

All the angles of a triangle are less than 60$$^o$$

Solution

Question 3

4 cm

10 cm

4 cm or 10 cm

None of these

Solution

Question 4

Right

Obtuse

Acute

None of these

Solution

Question 5

$$3, 4, 5$$

$$5, 5, 6$$

$$2, 3, 4$$

None of these

Solution

Question 6

is less than the sum of the two angles

should be an acute angle

is the largest angle of the triangle

is an angle with any measurement less than $$180^o$$

Question 7

$$\displaystyle 60^{0}$$

$$\displaystyle 70^{0}$$

$$\displaystyle 80^{0}$$

$$\displaystyle 55^{0}$$

Solution

Question 8

0

1

2

3

Solution

Question 9

$$40 \ m$$

$$42 \ m$$

$$41 \ m$$

$$46 \ m$$

Solution

Question 10

4 m, 3 m, 11 m

7 mm, 4 mm, 4 mm

3 cm, 1.1 cm, 5 cm

3 m, 4 m, 8 m

Solution

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