The Triangle and Its Properties Test

Result

The Triangle and Its Properties Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

In $$\Delta PQR$$, if $$\angle P=60^{o}$$, and $$\angle Q=40^{o}$$, then the exterior angle formed by producing $$QR$$ is equal to

A
$$60^{o}$$

B
$$120^{o}$$

C
$$100^{o}$$

D
$$80^{o}$$

Solution

Let $$QR$$ is extended to point $$S$$.
(Refer image)
In triangle $$PQR$$
$$\angle PRS=\angle P+\angle Q$$
$$\Rightarrow \angle PRS=60^{o}+40^{o}$$
$$\Rightarrow \angle PRS=100^{o}$$
Question 2
1 / -0

In a right-angled triangle $$ABC$$, if angle $$B = 90^o$$, then which of the following is true?

A
$$AB^2 = BC^2 + AC^2$$

B
$$AC^2 = AB^2 + BC^2$$

C
$$AB = BC + AC$$

D
$$AC = AB + BC$$

Solution

Hypotenuse is the longest side of triangle which is opposite to right angle.
By pythagoras theorm,
$$\text{(hypotenuse)}^2=\text{(side 1)}^2+\text{(side 2)}^2$$
$$\Longrightarrow AC^2 = AB^2 + BC^2$$
So, option $$B$$ is correct.
Question 3
1 / -0

Write the correct answer from the given four options.
The hypotenuse of a right triangle with its legs of lengths $$3x \times 4x$$ is

A
$$5x$$

B
$$7x$$

C
$$16x$$

D
$$25x$$

Solution

$$(Hypotenuse)^2 = (3x)^2 + (4x)^2 = 9x^2 + 16x^2 = 25x^2$$
$$Hypotenuse = \sqrt{25x^2} = 5x$$
Question 4
1 / -0

The measures of $$\angle x$$ and $$\angle y$$ in figure are respectively

A
$$30^{o},60^{o}$$

B
$$40^{o}, 40^{o}$$

C
$$70^{o}, 70^{o}$$

D
$$70^{o}, 60^{o}$$

Solution

$$120^0$$ is exterior of $$\angle R$$
$$\therefore \angle P+\angle Q=120^0$$
$$\Rightarrow 120^{o}=x+50^{o}$$
$$\Rightarrow x=120^{o}-50^{o}$$
$$\Rightarrow x=70^{o}$$
Now in $$\Delta PQR$$
$$x+y+50^{o}=180^{o}$$
$$\Rightarrow 70^{o}+y+50^{o}=180^{o}$$
$$\Rightarrow y=180^{o}-70^{o}-50^{o}$$
$$\Rightarrow y=60^{o}$$
Therefore, $$x=60^{o}$$ and $$y=70^{o}$$.
Hence, option $$D$$ is correct.
Question 5
1 / -0

If we join a vertex to a point on opposite side, which divides that side in the ratio $$1:1$$, then what is the special name of that line segment?

A
Median

B
Angle bisector

C
Altitude

D
Hypotenuse

Solution

Median from an vertex divides the opposite sides into ratio of $$1:1$$
So, special name of that segment is $$\text{Median}$$
Hence, option $$A$$ is correct.
Question 6
1 / -0

How many altitudes does a triangle have?

A
$$1$$

B
$$3$$

C
$$6$$

D
$$9$$

Solution

$$\textbf{Step-1: Represent the altitudes of a triangle using a diagram. }$$
$$\text{A triangle has three altitudes. From each vertex perpendicular to the opposite side can be drawn.}$$
$$\textbf{Hence, option - B is the correct answer.}$$
Question 7
1 / -0

Which of the following can be the length of the third side of triangle whose two sides measure $$18 cm$$ and $$14 cm $$?

A
$$4 \,cm$$

B
$$3 \,cm$$

C
$$5 \,cm$$

D
$$32 \,cm$$

Solution

Let $$y \,cm$$ be the third side of the triangle.
Hence,
$$\Rightarrow 18+14>y$$
$$\Rightarrow 32>y$$

$$18-14 <y$$
$$y>4 \ and\ 32>y$$
$$4<y<32$$

Therefore, the third side of a triangle can be $$5 cm$$.
Question 8
1 / -0

Which of the following figures will have its altitude outside the triangle?

A

B

C

D

Solution

In obtuse angled triangle, two of its altitudes lie outside the triangle.
Also, from figure it is clear that $$D$$ has its altitude outside triangle, which is an obtuse angled triangle.

Hence, option D is correct.
Question 9
1 / -0

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

A
Isosceles triangle

B
Obtuse angled triangle

C
Equilateral triangle

D
Right angled triangle

Solution
Question 10
1 / -0

In given $$\triangle ABC$$, AE, BF and CD are

A
Bisectors

B
Altitudes

C
Sides

D
Medians

Solution