MCQ Questions for Class 7 Maths The Triangle And Its Properties Quiz 2

A triangle with the sides measuring

$4$ cm,

$5$ cm and

$5$ cm is called

0%
an equilateral triangle
0%
an isosceles triangle
0%
a scalene triangle
0%
none of the above

Explanation

Given, the sides of the triangle are

$4$ cm,

$5$ cm and

$5$ cm

A triangle having two equal sides is called an isosceles triangle.

Here, two sides of the triangle are

$5$ cm and

$5$ cm. So, it is an isosceles triangle.

So, option B is correct.

A triangle with one right angle and two acute angles is called

0%
right angled triangle
0%
acute angled triangle
0%
equilateral triangle
0%
none of these

A triangle can have :

0%
one right angle
0%
two right angles
0%
three obtuse angles
0%
none of these

Explanation

Right angled triangle is a type of a triangle where one angle is right angle.

By angle sum property, sum of angles of a triangle

$= 180^{o}$

If two angles are right angles in a triangle, then according to angle sum property, third angle

$= 0^{o}$

This is not possible for a triangle.

So, other two angles have to be acute angle.

$A$ is the answer.

A triangle with the sides measuring

$5$ cm,

$6$ cm and

$4$ cm is called:

0%
an equilateral triangle
0%
an isosceles triangle
0%
a scalene triangle
0%
none of the above

In a right angled triangle, the other two angles are:

0%
acute
0%
obtuse
0%
right
0%
none of these

Explanation

An acute angle is an angle smaller than a right angle

$(90^{o}$ is called a right angle

$).$ Hence, in a right angled triangle the other two angles are acute.

The length of the hypotenuse of a right-angle triangle whose measure of two sides are 12 cm and

0.35 m is:

0%
37 cm
0%
3.72 cm
0%
0.372 cm
0%
37 m

Explanation

$0.35\, m\, =\, 0.35\, \times\, 100\, cm\, =\, 35\, cm$
For a right angle triangle using Pythagorus theorem we get,

$(Hypotenuse)^2\, =\, (side)^2\, +\, (side)^2$

$=\, (12)^2\, +\, (35)^2$

$= 144 + 1225$

$= 1369$

$Hypotenuse =$

$\sqrt{1369}\, =\, 37\, cm$

A triangle with one obtuse and two acute angles is called

0%
right angled triangle
0%
acute angled triangle
0%
obtuse angled triangle
0%
none

The triangle formed by

$BC=8.2 cm$ ,

$AC=7 cm$ and

$\displaystyle \angle C = 120^{\circ}$ is-

0%
An obtuse angled triangle
0%
An acute angle triangle
0%
A right angled triangle
0%
None of these

Explanation

In△ABC,

$BC=8.2cm,AC=7cm$ and

$\angle C=120°$

Here, we can see triangle contain one obtuse angle.

So,△ABC, is an obtuse angled triangle

Option A is the correct answer.

Sum of the lengths of any two sides of a triangle is always ____ than the length of the third side.

0%
less than
0%
equal to
0%
greater than
0%
None of these

If two angles in a triangle are 75

$\displaystyle ^{\circ}$ and 95

$\displaystyle ^{\circ}$ then the third angle is__

0%
30 $\displaystyle ^{\circ}$
0%
20 $\displaystyle ^{\circ}$
0%
10 $\displaystyle ^{\circ}$
0%
40 $\displaystyle ^{\circ}$

Explanation

Because by angle sum property, the sum of angles is

$180^o$ .

Let n be the third angle.

$\therefore 75\displaystyle ^{\circ}$ + 95

$\displaystyle ^{\circ}$ + n = 180

$\displaystyle ^{\circ}$

$\displaystyle \Rightarrow$ n =10

$\displaystyle ^{\circ}$

$\displaystyle \therefore$ Third angle = 10

$\displaystyle ^{\circ}$

A quadrilateral is having _____.

0%
one diagonal
0%
two diagonals
0%
three diagonals
0%
four diagonals

Explanation

A quadrilateral is a four-sided polygon.

Here,

$ABCD$ is a quadrilateral having four sides

$AB,BC,CD$ and

$AD$

Diagonal is a line segment that goes from one corner to another.

The diagonals of quadrilateral

$ABCD$ are

$AC$ and

$BD$ .

$\therefore$ A quadrilateral is having two diagonals.

1263853_405987_ans_f59566df9fc04970a5217c38782daf3e.jpeg

The interior of a triangle is

0%
the intersection of three lines
0%
the union of three line segments
0%
the set of the intersection of interiors of the angles of triangle
0%
none of these

Can the three sides of length

$6 cm, 5 cm,$ and

$3 cm$ form a triangle?

0%
Yes
0%
No
0%
Sometimes
0%
None

Explanation

Taking two sides at a time to check the inequality property of a triangle that is the sum of two sides of a triangle is always greater than the third side.

(1)

$(6 + 5) =11 > 3$ {Satisfying}
(2)

$(5 + 3)= 8 > 6$ {Satisfying}
(3)

$(3 + 6) =9 > 5$ {Satisfying}
Hence, they can form a triangle.

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

0%
Isosceles
0%
Scalene
0%
Equilateral
0%
Right-angled

Explanation

$\displaystyle \angle A=\frac { 1 }{ 2 } \left( \angle B+\angle C \right)$

$\displaystyle \angle A+\angle B+\angle C=\frac { 1 }{ 2 } \left( \angle B+\angle A \right)$

$\displaystyle or\quad \angle B+\angle C={ 90 }^{ o }or\angle A={ 90 }^{ o }$

1294484_378222_ans_d40cbe0215574ff382cb3359c2a17765.png

In a

$\displaystyle \Delta ABC$ , if

$\displaystyle AC^{2} = AB^{2} + BC^{2}$ then the right angle is at__

0%
C
0%
B
0%
A
0%
None of these

Explanation

Pythagoras theorem,

$\Rightarrow$

$(Hypotenuse)^2=(One\,side)^2+(second\,side)^2$ ---- ( 1 )

$\triangle ABC,$

$\Rightarrow$

$(AC)^2=(AB)^2+(BC)^2$ [ Given ] ----- ( 2 )

Comparing ( 1 ) and ( 2 ) we get,

$\Rightarrow$

$AC$ is the hypotenuse of a triangle.

Hypotenuse is the longest side of a right-angled triangle, opposite the right angle.

So, opposite angle of hypotenuse

$AC$ is

$B.$

$\therefore$

$B$ is right angle.

$\Rightarrow$ In

$\triangle ABC$ if

$AC^2=AB^2+BC^2$ then the right angle is at

$B.$

1370113_404672_ans_9a92d8d1a7e441109789afc5feec2486.png

All equilateral triangles have ___ sides and ____ angles equal.

0%
two, two
0%
three, three
0%
three , two
0%
two, three

Explanation

A triangle with all sides equal and all the three angles equal to

$60^\circ$ is called an Equilateral triangle.

Thus, option

$B$ is correct.

We use ........... formula to find the lengths of the right angled triangles.

0%
Pythagoras theorem
0%
Postulate theorem
0%
Thales theorem
0%
None of the above

Explanation

$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$ is the formula used to find the lengths of the right angled triangles. This formula was named after the mathematician named Pythagoras called Pythagoras theorem .
Therefore, A is the correct answer.

Angles opposite to ____ sides of an isosceles triangles are equal.

0%
equal
0%
unequal
0%
any two
0%
none of these

In Pythagoras theorem in right angled triangle the longest side is called the

0%
Hypotenuse
0%
Height
0%
Perpendicular
0%
Bisector

Explanation

Longest side is called Hypotenuse and its is opposite to the right angle.

In the attached figure

$AC$ is Hypotenuse.

A triangle whose........... angle(s) is

$\displaystyle { 90 }^{ o }$ is called a right angled triangle.

0%
$0$
0%
$3$
0%
$2$
0%
$1$

Explanation

A triangle whose one angle is

$\displaystyle { 90 }^{ o }$ is called a right angled triangle.

In Pythagoras theorem the right angled triangle is also called a

0%
Acute angled triangle
0%
Scalene angled triangle
0%
Reflex angled triangle
0%
Straight angled triangle

Explanation

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.

For given figure, the formula for Pythagoras theorem is:

0%
$\displaystyle { a }^{ 2 }-{ b }^{ 2 }={ c }^{ 2 }$
0%
$\displaystyle { c }^{ 2 }+{ b }^{ 2 }={ a }^{ 2 }$
0%
$\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$
0%
$\displaystyle { a }^{ 2 }+{ c }^{ 2 }={ b }^{ 2 }$

Explanation

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

If all the angles of a triangle measure less than

$\displaystyle { 90 }^{ o }$ , then such a triangle is called ........

0%
Right angled triangle
0%
Obtuse angled triangle
0%
Acute angled triangle
0%
None of these

Explanation

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.

How do you know the triangle is right angled?

0%
The triangle is right angled when the three sides of a triangle make $\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$
0%
The triangle is right angled when the three sides of a triangle do not make $\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$
0%
The triangle is not right angled when the three sides of a triangle make $\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$
0%
The three sides of a triangle are all same.

Explanation

If a triangle is right triangle then the square of longest side is equal to the sum of squares of other two sides.

$a,b,c$ are the sides with

$c$ as longest side then

$a^2+b^2=c^2$

So option

$A$ is correct.

__________ triangle has two sides of equal length.

0%
Equilateral
0%
Scalene
0%
Isosceles
0%
Acute

Explanation

$(A)$ 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.

A ______ triangle has no congruent sides.

0%
isosceles
0%
equilateral
0%
acute
0%
scalene

A ______ triangle has no equal angles.

0%
isosceles
0%
equilateral
0%
acute
0%
scalene

Which angle of a triangle is a right angle?

0%
Angle C
0%
Angle A
0%
Angle B
0%
None of the above

Explanation

From the geometry of the figure it is clear that

$\angle B$ is right angle.

So option

$C$ is correct.

Identify the scalene triangle.

Explanation

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.

What is the length of

$BC$ in an equilateral triangle?

0%
1
0%
2
0%
3
0%
4

Explanation

An equilateral triangle has all three sides of equal length.
So,

$AB = AC = BC = 4$ .

CBSE Questions for Class 7 Maths The Triangle And Its Properties Quiz 2 - MCQExams.com

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Practice Class 7 Maths Quiz Questions and Answers

CBSE Questions for Class 7 Maths The Triangle And Its Properties Quiz 2 - MCQExams.com

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Practice Class 7 Maths Quiz Questions and Answers

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