MCQ Questions for Class 7 Maths The Triangle And Its Properties Quiz 4

An ______ angle is an angle created by the side of a shape and a line extended from an adjacent side.

0%
interior
0%
exterior
0%
opposite
0%
same

Find the name of the triangle.

0%
acute isosceles triangle
0%
acute scalene triangle
0%
acute obtuse triangle
0%
acute equilateral triangle

In the following figure, what is the value of

$y$ in terms of

$x$ ?

0%
$x + 80$
0%
$80 - x$
0%
$x + 100$
0%
$x - 100$
0%
$100 - x$

Explanation

In the given figure,

$y$ is an exterior angle where as

$x$ and

$100$ is are interior angles of the triangle.
We know, exterior angle is equal to sum of two opposite interior angles.
So as per the problem,

${ y= } { x } + { 100 }$

Find the measure of the missing angle in the triangle below.

0%
$35^o$
0%
$40^o$
0%
$45^o$
0%
$50^o$
0%
$55^o$

Explanation

By angle sum property, the sum of angles is

$180^o$ .

If we subtract the two given angles from

$180^0$ , the result will be the missing angle which is

$= 180^0 - 95^0 - 35^0 = 50^0$ .

Therefore, the missing angle is

$50^0$ .

In a triangle

$ABC$ ,

$AB=AC$ , then

$\triangle ABC$ is a/an ............ triangle.

0%
right angled
0%
equilateral
0%
isosceles
0%
scalene

Explanation

Given,

$\triangle ABC, AB = AC$

We know, if two sides of a triangle are equal then the triangle is an isosceles triangle.

Thus,

$\triangle ABC$ is an isosceles triangle.

Hence, option

$C$ is correct.

Which of the following has no lines of symmetry ?

0%
A scalene triangle
0%
An isosceles triangle
0%
An equilateral triangle
0%
All of these

Explanation

$\Rightarrow$ An equilateral triangle has three lines of symmetry.

$\Rightarrow$ An Isosceles triangle has one line of symmetry.

$\Rightarrow$ A scalene triangle does not have any line of symmetry.

$\therefore$ Correct answer is option

$A$ .

$a, b$ and

$c$ are the sides of a triangle, then __________.

0%
$a-b > c$
0%
$c > a +b$
0%
$c =a+b$
0%
$b< c+a$

Explanation

This problem is totally based on the theorem which says any triangle with sides let say

$a , b ,c$ , then

$a+b > c$ and

$c+b > a$ and

$c+a > b$

Therefore, option D is correct.

In the given figure, ABCD is a trapezium in which AB

$=7$ cm, AD

$=$ BC

$=5$ cm, DC

$=$ x cm and the distance between AB and DC is

$4$ cm. Then the value of x is ____________.

0%
$13$
0%
$16$
0%
$19$
0%
Cannot be determined

Explanation

$\triangle ALD$ and

$\triangle BMC$ :

$DL^2=AD^2-AL^2=5^2-4^2=9\\ \Rightarrow LD=3\ cm$

Similarly,

$MC=3\ cm$

$\therefore x=DL+LM+MC$ (Length of

$LM=AB=7\ cm$ )

$x=3+7+3=13\ cm$

In figure,

$\angle C = 90^\circ$ in isosceles triangle

$\Delta ABC$ , then

$AB^2 =$ ................

0%
$\sqrt 2 BC^2$
0%
$2BC^2$
0%
$BC^2$
0%
$4 BC^2$

Explanation

$\Delta ACB$ ,

Given:

$\angle C = 90^\circ$

Also,

$AC = BC$ [

$\Delta ABC$ is isosceles]

$\therefore AB^2 = AC^2 + BC^2$ [By Pythagoras theorem]

$\therefore AB^2 = BC^2 + BC^2$

$\therefore AB^2 = 2BC^2$

In a triangle, the angles are in ratio

$1: 3: 2$ . Find the difference between the greatest and smallest angle of the triangle.

0%
$10^o$
0%
$70^o$
0%
$60^o$
0%
$20^o$

Explanation

Given, the angles are in the ratio

$1:3:2$ .

Let the angles be

$x,3x$ and

$2x$ .

Using angle sum property of triangle,

$x+3x+2x={ 180 }^{ \circ }\\ \Rightarrow 6x={ 180 }^{ \circ }\\ \Rightarrow x={ 30 }^{ \circ }.$

So the angles are :

$x={ 30 }^{ \circ }$ ,

$3x=3\times { 30 }^{ \circ }={ 90 }^{ \circ }$

and

$2x=2\times { 30 }^{ \circ }={ 60 }^{ \circ }$ .

Therefore, the difference between the greatest and the smallest angle

$={ 90 }^{ \circ }-{ 30 }^{ \circ }={ 60 }^{ \circ }$ .

Hence, option

$C$ is correct.

From the given figure BD=______________.

0%
$x+y$
0%
$\sqrt{xy}$
0%
$xy$
0%
$\sqrt{x+y}$

Explanation

By the theorem(Perpendicular drawn to the hypotenuse of right angled triangle), we get

$BD^2=AD \times CD =xy$

$\therefore BD=\sqrt{xy}$

Which of the following can be the sides of a right angled triangle ?

0%
$35, 17,18$
0%
$39, 19,18$
0%
$35, 27,18$
0%
$41,40,9$

Explanation

We know that in a right angle triangle,

The sum of the squares on two sides of a triangle is equal to the square on the third side, then the triangle is a right angle.

$Base^2 + Prependicular^2 =Hypotenuse^2$

Now, we go to the options,

$18^2+17^2$ is not equal to

$35^2$ so leave this option.

$19^2+18^2$ is not equal to

$39^2$ so leave this option.

$27^2+18^2$ is not equal to

$35^2$ so leave this option.

$40^2+9^2$ is equal to

$41^2$ so right this option.

Hence, all option is incorrect.

Now , we take the triplet

$41$ ,

$40$ ,

$9$

$40^2+9^2=1681$

$$40^2+9^2=41^2$$

Hence,

$41$ ,

$40$ ,

$9$ are the sides of a right angle triangle

option

$D$ is correct.

If you place a ladder against a wall at an angle, what type of a triangle will you get?

0%
Equilateral triangle
0%
Right angle triangle
0%
Isosceles triangle
0%
Scalene triangle

Explanation

Here

$AO$ is wall and

$AB$ is ladder.

Hence,irrespective of what

$\theta$ is,

$\angle AOB$ will always be

${ 90 }^{ \circ }$ .

$\therefore$ Triangle will always be right-angled.

1005667_1064521_ans_c3e5f8421f484fd3b876f9523708384e.png

$\Delta ABC;\;m \angle B=90^{\circ};\;AB=5\;cm$ and

$AC=13$ then,

$BC=....$

0%
$10$
0%
$18$
0%
$8$
0%
$12$

Explanation

Since in a triangle

$ABC$ angle B is given to be 90°.

So by pythagoras theorem we have

$BC^2 = AC^2-AB^2$

$\Rightarrow$

$BC^2 = 13^2-5^2$

$\Rightarrow$

$BC= 12$

$\triangle ABC$ is

$\angle B$ is right angle. If

$AB = a=16$ and

$BC = c=12$ then

$AC = b=$ __________

0%
$8$
0%
$18$
0%
$20$
0%
$28$

Explanation

Given:

$\angle$

$B$ is

$90$

$^{\circ}$

$a = 16$

$c = 12$

$\therefore$ using Pythagoras theorem

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

$16^{2}+12^{2}=b^{2}$

$256+144=b^{2}$

$400=b^{2}$

$\therefore$

$b = 20.$

If the square of the hypotenuse of an isosceles right triangle is

$128 \ cm^2$ . The length of other two sides is 8 cm.

0%
True
0%
False

Explanation

Let the two equal side of right angled isosceles triangle, right angled at Q be k cm.

$h^2=128$

So, we get,

$PR^2=PQ^2+QR^2$

$h^2=k^2+k^2$

$128=2k^2$

$k^2=64$

$k=8$

Therefore, the length of other two sides is 8 cm.

1480080_1332175_ans_5c1e86aea00043f68f2de3388ae62f0f.PNG

Find the hypotenuse of right angled triangle if the other sides are

$3,4$ respectively.

0%
5
0%
3
0%
2
0%
1

Explanation

Given sides of triangle are

$3,4$

From Pytagorous theorm ,

$AC^2=AB^2+BC^2\\AC^2=3^2+4^2\\AC^2=9+16\\AC^2=25\\AC=\sqrt{25}\\AC=5$

Which of the following are angles of Obtuse angled triangle?

0%
$30^{o},90^{o},60^{o}$
0%
$30^{o},70^{o},80^{o}$
0%
$120^{o},20^{o},40^{o}$
0%
$90^{o},45^{o},45^{o}$

Explanation

Ans- From given angles obtuse angled triangle pair is

$120^{\circ},20^{\circ},40^{\circ}$

obtuse angle:- Angle greater than

$90^{\circ}$ but smaller than

$180^{\circ}$

1208244_1361492_ans_a5454446c38c4e91a971171d355a9ada.JPG

Find hypotenuse of right angled triangle if the sides are

$12,4\sqrt 3$

0%
$8\sqrt 3$
0%
$4\sqrt 3$
0%
$6\sqrt 3$
0%
$12\sqrt 3$

Explanation

The hypotenuse is given by

$\sqrt {12^2+(4\sqrt 3)^2}\\\sqrt {144+48}\\\sqrt {192}=8\sqrt 3$

A right angled triangle has

$24,7cm$ as its sides . What will be its hypotenuse?

0%
$25$ cm
0%
$37$ cm
0%
$29$ cm
0%
$53$ cm
0%
None of these

Explanation

The sides of right angled triangle are

$24,7cm$

The hypotenuse is given as

$a^2+b^2=c^2\\7^2+24^2=c^2\\49+576=c^2\\c^2=625\\c=\sqrt {625}\\c=25cm$

Which of the following statements are true (T) and which are false (F) :
A triangle can have at most one obtuse angles.

0%
True
0%
False

Is the following statement true (T) and which are false (F)?
All the angles of a triangle can be equal to

$60^{\circ}$ .

0%
True
0%
False

Explanation

Given all the angles are equal to

$60^o$ .

We know, by angle sum property, the sum of all the angles of a triangle is

$180^o$ .

Then,

$60^o+60^o+60^o=120^o+60^o=180^o$ .

Hence, it is possible for all the angles of a triangle to be equal to

$60^o$ .

That is, the statement is true and option

$A$ is correct.

In the following, state if the statement is true(T) or false(F).
Each acute triangle is equilateral.

0%
True
0%
False

Explanation

False

A triangle with angle

$50^o,60^o,70^o$ is an acute angle triangle, but it isn't an equilateral triangle.

Sum of any two angles of a triangle is always greater than the third angle.

0%
True
0%
False

In a right triangle, the square of the third side(larger side) is equal to the sum of squares of other two sides.

0%
True
0%
False

A right-angled triangle may have all sides equal.

0%
True
0%
False

If two angles of a triangle are

$60^o$ each, then the triangle is

0%
Isosceles but not equilateral
0%
Scalene
0%
Equilateral
0%
Righe-angled

Explanation

Let triangle

$ABC$ , in which the base angle is

$60^o$

$\angle A + \angle B + \angle C = 180^o$

$\Longrightarrow \angle A = 180^o - 60^o - 60^o$

$\Longrightarrow \angle A = 60^o$
Therefore,

$\Delta ABC$ is

$60^o$ equilateral triangle.

An isosceles right triangle has area

$8\ cm^{2}$ . The length of its hypotenuse is

0%
$\sqrt{32} cm$
0%
$\sqrt{16} cm$
0%
$\sqrt{48} cm$
0%
$\sqrt{24} cm$

Explanation

Explanation:

Let height of triangle =

$h$

As the triangle is isosceles,

Let base = height =

$h$

According to the question, Area of triangle =

$8cm^{2}$

$\implies \dfrac{1}{2} \times Base \times Height = 8$

$\implies \dfrac{1}{2} \times h \times h = 8$

$\implies h^{2}= 16$

$\implies h = 4cm$

Base = Height =

$4cm$

Since the triangle is right angled,

$Hypotenuse^{2} = Base^{2} + Height^{2}$

$\implies Hypotenuse^{2} = 4^{2} + 4^{2}$

$\implies Hypotenuse^{2} = 32$

$\implies Hypotenuse = \sqrt{32}$

Hence, Options

$A$ is the correct answer.

A triangle formed by the sides of lengths

$4.5\ cm,6\ cm,$ and

$4.5\ cm$ is

0%
scalene
0%
isosceles
0%
equilateral
0%
none of these

Explanation

A triangle formed by the sides of lengths

$4.5\ cm,6\ cm,$ and

$4.5\ cm$ is isosceles. As, two sides are of equal length.

State whether the following statements are true (T) or false (F):
If all three sides of a triangle are equal, then it is called a scalene triangle.

0%
True
0%
False

CBSE Questions for Class 7 Maths The Triangle And Its Properties Quiz 4 - 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 4 - MCQExams.com

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Practice Class 7 Maths Quiz Questions and Answers

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