The Triangle and Its Properties Test

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The Triangle and Its Properties Test - 10

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Question 1
1 / -0

A ______ triangle has no equal angles.

A
isosceles

B
equilateral

C
acute

D
scalene

Solution

A scalene triangle has all angles and sides unequal.
Question 2
1 / -0

What is the length of $$BC$$ in an equilateral triangle?

A
1

B
2

C
3

D
4

Solution

An equilateral triangle has all three sides of equal length.
So, $$AB = AC = BC = 4$$.
Question 3
1 / -0

Identify the scalene triangle.

A

B

C

D

Solution

Scalene triangles are triangles with all three sides of different lengths and all three angles of different measure.
Option $$A$$ has all sides of same length.
Option $$B$$ and $$D$$ have two sides of same length.
So, only option $$C$$ is correct, where all $$3$$ sides and angles are different.
Question 4
1 / -0

If one acute angle of the right angled triangle is half of the other, then the smallest angle is:

A
$$\displaystyle { 90 }^{ o }$$

B
$$\displaystyle { 60 }^{ o }$$

C
$$\displaystyle { 40 }^{ o }$$

D
$$\displaystyle { 30 }^{ o }$$

Solution

Let the acute angle be $$x$$.
Given, the acute angle is half of the other.
Then the other angle is $$2x$$.

We know, by angle sum property, the sum of angles of a triangle is $$\displaystyle { 180 }^{ o }$$.
$$\implies$$ $$\displaystyle { 90 }^{ o }+2x+x={ 180 }^{ o }$$
$$\implies$$ $$\displaystyle 3x={ 180 }^{ o }-{ 90 }^{ o }$$
$$\implies$$$$\displaystyle x=\frac { { 90 }^{ o } }{ 3 } $$
$$\implies$$$$\displaystyle x={ 30 }^{ o }$$.

Hence, the angles are:
$$90^o, x=30^o$$ and $$2x=2\times30^o=60^o$$.

Here, $$30^o$$ is the smallest angle.

Therefore, option $$D$$ is correct.
Question 5
1 / -0

If a triangle is given $$\displaystyle \Delta PQR$$, then ______ is the hypotenuse.

A
PQ

B
PR

C
QP

D
RQ

Solution

Given in the figure Sides PQ & RQ are shorter Than the side PR , and in a right angled triangle The longest side is the Hypotenuse.
So, PR is the Hypotenuse.
Therefore, B is the correct answer.
Question 6
1 / -0

In a triangle, if the square of one side is equal to the sum of the squares of the other two sides , then the angle opposite the first side is a.

A
Less than a right angle

B
More than a right angle

C
Not a right angle

D
Right angle

Solution

If $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$, c is the hypotenuse and angle opposite to the hypotenuse is a right angle in Pythagoras theorem , so the angle opposite the first side that is the hypotenuse is a right angle.
Therefore, D is the correct answer.
Question 7
1 / -0

Find the name of the triangle.

A
isosceles

B
equilateral

C
scalene

D
acute

Solution

The name of the triangle is scalene triangle, because all the sides are different.
Question 8
1 / -0

Which one of the following figure is not a scalene triangle?

A

B

C

D

Solution

The second option is not a scalene triangle, because it has $$2$$ equal sides.
Question 9
1 / -0

A triangle that has an angle greater than ____ is called as obtuse triangle.

A
$$30^{o}$$

B
$$60^{o}$$

C
$$80^{o}$$

D
$$90^{o}$$

Solution

A triangle that has an angle greater than $$90^{o}$$ is called as obtuse triangle.
Question 10
1 / -0

A scalene triangle has three different side lengths and three different ______.

A
radius

B
angles

C
arc

D
symmetry

Solution

A scalene triangle has three different side lengths and three different angles.