The Triangle and Its Properties Test

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The Triangle and Its Properties Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

A triangle whose........... angle(s) is $$\displaystyle { 90 }^{ o }$$ is called a right angled triangle.

A
$$0$$

B
$$3$$

C
$$2$$

D
$$1$$

Solution

A triangle whose one angle is $$\displaystyle { 90 }^{ o }$$ is called a right angled triangle.
Question 2
1 / -0

What is the name of the closed figure with four sides?

A
Hexagon

B
Triangle

C
Pentagon

D
Quadrilateral

Solution

A quadrilateral is a closed figure having four sides.
Therefore, $$D$$ is the correct answer.
Question 3
1 / -0

Define Pythagoras theorem.

A
In a right angled triangle , square of a hypotenuse is not equal to the sum of the squares of two sides.

B
In a right-angled triangle, the square of a hypotenuse is equal to the sum of the squares of the other two sides.

C
In a right angled triangle , hypotenuse is equal to the sum of two sides.

D
In a triangle , square of a side is equal to the square of another side.

Solution

In a right angled triangle ,square of hypotenuse (longest side) is equal to the sum of squares of other two sides.
In $$\triangle ABC$$
$${ \left( AC \right) }^{ 2 }{ =\left( AB \right) }^{ 2 }+{ \left( BC \right) }^{ 2 }$$
Question 4
1 / -0

In Pythagoras theorem the right angled triangle is also called a

A
Acute angled triangle

B
Scalene angled triangle

C
Reflex angled triangle

D
Straight angled triangle

Solution

A scalene angled triangle has no sides or angles that are the same.
For Eg: The sides of a triangle are in the ratio $$6:8:10$$. So triangle with different sides or angles is called Scalene Angled Triangle.
Question 5
1 / -0

For given figure, the formula for Pythagoras theorem is:

A
$$\displaystyle { a }^{ 2 }-{ b }^{ 2 }={ c }^{ 2 }$$

B
$$\displaystyle { c }^{ 2 }+{ b }^{ 2 }={ a }^{ 2 }$$

C
$$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$

D
$$\displaystyle { a }^{ 2 }+{ c }^{ 2 }={ b }^{ 2 }$$

Solution

The formula of Pythagoras theorem for the right angled triangles is $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$.
The diagram shows a right angled triangle which is right angeled at C. So, we use $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$ to find the unknown length.
Where,
$$a = $$ Height
$$b = $$ base
$$c = $$ Hypotenuse
Question 6
1 / -0

If all the angles of a triangle measure less than $$\displaystyle { 90 }^{ o }$$, then such a triangle is called ........

A
Right angled triangle

B
Obtuse angled triangle

C
Acute angled triangle

D
None of these

Solution

If all the angles of a triangle measure less than $$\displaystyle { 90 }^{ o }$$, then such a triangle is called acute angled triangle. For eg: An equilateral triangle with all the angles equal to $$\displaystyle { 60 }^{ o }$$ is acute angled triangle.
Question 7
1 / -0

How do you know the triangle is right angled?

A
The triangle is right angled when the three sides of a triangle make $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$

B
The triangle is right angled when the three sides of a triangle do not make $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$

C
The triangle is not right angled when the three sides of a triangle make $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$

D
The three sides of a triangle are all same.

Solution

If a triangle is right triangle then the square of longest side is equal to the sum of squares of other two sides.
If $$a,b,c$$ are the sides with $$c$$ as longest side then
$$a^2+b^2=c^2$$
So option $$A$$ is correct.
Question 8
1 / -0

Which angle of a triangle is a right angle?

A
Angle C

B
Angle A

C
Angle B

D
None of the above

Solution

From the geometry of the figure it is clear that $$\angle B$$ is right angle.
So option $$C$$ is correct.
Question 9
1 / -0

__________ triangle has two sides of equal length.

A
Equilateral

B
Scalene

C
Isosceles

D
Acute

Solution

$$(A)$$ Equilateral triangle has all three sides equal.
$$(B)$$ Scalene triangle has all three sides unequal.
$$(C)$$ Isosceles triangle has two sides of equal length.
$$(D)$$ Acute triangle is a type of triangle which depends upon the angles.
So, option $$C$$ is correct.
Question 10
1 / -0

A ______ triangle has no congruent sides.

A
isosceles

B
equilateral

C
acute

D
scalene

Solution

A scalene triangle has no congruent sides, all sides are different.

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The Triangle and Its Properties Test - 9

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Question 1

$$0$$

$$3$$

$$2$$

$$1$$

Solution

Question 2

Hexagon

Triangle

Pentagon

Quadrilateral

Solution

Question 3

In a right angled triangle , square of a hypotenuse is not equal to the sum of the squares of two sides.

In a right-angled triangle, the square of a hypotenuse is equal to the sum of the squares of the other two sides.

In a right angled triangle , hypotenuse is equal to the sum of two sides.

In a triangle , square of a side is equal to the square of another side.

Solution

Question 4

Acute angled triangle

Scalene angled triangle

Reflex angled triangle

Straight angled triangle

Solution

Question 5

$$\displaystyle { a }^{ 2 }-{ b }^{ 2 }={ c }^{ 2 }$$

$$\displaystyle { c }^{ 2 }+{ b }^{ 2 }={ a }^{ 2 }$$

$$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$

$$\displaystyle { a }^{ 2 }+{ c }^{ 2 }={ b }^{ 2 }$$

Solution

Question 6

Right angled triangle

Obtuse angled triangle

Acute angled triangle

None of these

Solution

Question 7

The triangle is right angled when the three sides of a triangle make $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$

The triangle is right angled when the three sides of a triangle do not make $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$

The triangle is not right angled when the three sides of a triangle make $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$$

The three sides of a triangle are all same.

Solution

Question 8

Angle C

Angle A

Angle B

None of the above

Solution

Question 9

Equilateral

Scalene

Isosceles

Acute

Solution

Question 10

isosceles

equilateral

acute

scalene

Solution

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