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CBSE Questions for Class 7 Maths The Triangle And Its Properties Quiz 4 - MCQExams.com
CBSE
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.
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interior
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exterior
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opposite
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same
Explanation
An exterior angle is an angle created by the side of a shape and a line extended from an adjacent side.
Example:
Find the name of the triangle.
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acute isosceles triangle
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acute scalene triangle
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acute obtuse triangle
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acute equilateral triangle
Explanation
The given triangle is an acute equilateral triangle, because the three angles are equal.
In the following figure, what is the value of $$y$$ in terms of $$x$$?
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$$x + 80$$
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$$80 - x$$
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$$x + 100$$
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$$x - 100$$
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$$100 - x$$
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.
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$$35^o$$
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$$40^o$$
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$$45^o$$
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$$50^o$$
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$$55^o$$
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.
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right angled
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equilateral
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isosceles
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scalene
Explanation
Given,
In $$\triangle ABC, AB = AC$$
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 ?
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A scalene triangle
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An isosceles triangle
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An equilateral triangle
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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 $$A$$.
If $$a, b$$ and $$c$$ are the sides of a triangle, then __________.
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$$a-b > c$$
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$$c > a +b$$
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$$c =a+b$$
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$$b< c+a$$
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 ____________.
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$$13$$
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$$16$$
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$$19$$
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Cannot be determined
Explanation
In $$\triangle ALD$$ 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 $$AB^2 = $$ ................
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$$\sqrt 2 BC^2$$
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$$2BC^2$$
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$$BC^2$$
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$$4 BC^2$$
Explanation
In $$\Delta ACB$$,
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.
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$$10^o$$
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$$70^o$$
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$$60^o$$
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$$20^o$$
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 d
ifference between the greatest and the smallest angle $$={ 90 }^{ \circ }-{ 30 }^{ \circ }={ 60 }^{ \circ }$$.
Hence, option $$C$$ is correct.
From the given figure BD=______________.
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$$x+y$$
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$$\sqrt{xy}$$
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$$xy$$
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$$\sqrt{x+y}$$
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 ?
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$$ 35, 17,18$$
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$$ 39, 19,18$$
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$$ 35, 27,18$$
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$$ 41,40,9$$
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,
A) $$18^2+17^2 $$ is not equal to $$35^2$$ so leave this option.
B) $$19^2+18^2$$ is not equal to $$39^2$$
so leave this option.
C) $$27^2+18^2$$ is not equal to $$35^2$$
so leave this option.
D)$$40^2+9^2 $$ 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?
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Equilateral triangle
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Right angle t
riangle
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Isosceles t
riangle
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Scalene t
riangle
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.
In $$\Delta ABC;\;m \angle B=90^{\circ};\;AB=5\;cm$$ and $$AC=13$$ then, $$BC=....$$
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$$10$$
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$$18$$
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$$8$$
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$$12$$
Explanation
Since in a triangle $$ABC$$ angle B is given to be 90°.
So by pythagoras theorem we have
$$BC^2 = AC^2-AB^2$$
$$\Rightarrow$$ $$BC^2 = 13^2-5^2 $$
$$\Rightarrow$$ $$BC= 12$$
In $$\triangle ABC$$ is $$\angle B$$ is right angle. If $$AB = a=16$$ and $$BC = c=12$$ then $$AC = b=$$ __________
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$$8$$
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$$18$$
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$$20$$
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$$28$$
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.
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True
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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.
Find the hypotenuse of right angled triangle if the other sides are $$3,4$$ respectively.
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5
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3
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2
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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?
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$$30^{o},90^{o},60^{o}$$
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$$30^{o},70^{o},80^{o}$$
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$$120^{o},20^{o},40^{o}$$
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$$90^{o},45^{o},45^{o}$$
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 $$180^{\circ}$$
Find hypotenuse of right angled triangle if the sides are $$12,4\sqrt 3$$
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$$8\sqrt 3$$
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$$4\sqrt 3$$
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$$6\sqrt 3$$
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$$12\sqrt 3$$
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?
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$$25$$ cm
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$$37$$ cm
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$$29$$ cm
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$$53$$ cm
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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.
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True
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False
Is the following statement true (T) and which are false (F)?
All the angles of a triangle can be equal to $$ 60^{\circ}$$.
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True
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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.
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True
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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.
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True
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False
Explanation
Sum of any two angles of a triangle is may or may not be greater than the third angle.
In a right triangle, the square of the
third side(larger side) is equal to the
sum of squares of other two sides.
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True
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False
Explanation
True.
In a right-angled triangle, the square of the third side that is the larger side is equal to the sum of squares of other two sides.
A right-angled triangle may have all sides equal.
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True
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False
Explanation
False
A right-angled triangle may have two sides equal.
Also Pythagoras theorem cannot be satisfied by having all sides equal.
If two angles of a triangle are $$60^o$$ each, then the triangle is
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Isosceles but not equilateral
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Scalene
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Equilateral
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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
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$$\sqrt{32} cm$$
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$$\sqrt{16} cm$$
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$$\sqrt{48} cm$$
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$$\sqrt{24} cm$$
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
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scalene
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isosceles
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equilateral
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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.
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True
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False
Explanation
If all three sides of a triangle are equal, then it is called an equilateral triangle. Hence, the given statement is False.
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