MCQ Questions for Class 9 Maths Triangles Quiz 10

The sum of lengths of any two sides of a triangle is always_________the third side.

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

Explanation

The sum of lengths of any two sides of a triangle is always greater than the third side.
For e.g.. in

$\triangle ABC$ , we have

$AC+BC>AB$ .

If the angles of a triangle are

$30^{\circ},60^{\circ},90^{\circ}$ , then what is the ratio of corresponding sides?

0%
$\;1\,\colon\,2\,\colon\,3$
0%
$\;1\,\colon\,1\,\colon\,\sqrt{2}$
0%
$\;1\,\colon\,\sqrt{3}\,\colon\,3$
0%
$\;1\,\colon\,\sqrt{2}\,\colon\,2$

Explanation

Since the side opposite to the greatest angle is the greatest and the ratio of sides

$=$ Ratio of corresponding angles

Thus, the ratio of corresponding sides

$=30\,\colon\,60\,\colon\,90=1\,\colon\,2\,\colon\,3$ .

The side opposite to an obtuse angle of a triangle is

0%
Smallest
0%
Greatest
0%
Half of the perimeter
0%
None of these

Explanation

Angles between ${90}^{o}$ and ${180}^{o}$ are obtuse angles.

Since, sum of angles in a triangle $= {180}^{o}$

If one angle is obtuse, it will be the greatest angle as the other two angles will be acute angles such that the sum of the interior angles is ${180}^{o} .$

The angles opposite to the sides will also have the same relation.

Hence, the side opposite to the obtuse angle will be the greatest side of the triangle.

State the property by which

${\triangle }$ ADB

${\cong }$

${\triangle }$ ADC in the following figure.

0%
SAS property
0%
SSS property
0%
RHS property
0%
ASA property

Explanation

$AB=AC$ (Given)

$\angle BAD=\angle CAD$ (given)

$AD=AD$ (common)

$\therefore \triangle ADB\cong \triangle ADC$

$SAS$ property.

If a, b and c are the sides of a

$\Delta$ le then

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

Explanation

$b < c + a$

$\because$ Sum of any two sides is greater than the third side.

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

$\Delta$ ABC is congruent of

$\Delta$ DEF, if

0%
AB = 4 = DE, AC = 6 = DF, $\angle$ A = $\angle$ D
0%
AB = 4 = DE, AC = 6 = DF, $\angle$ B = $\angle$ E
0%
AB = 6 = DE, AC = 4 = DF, $\angle$ C = $\angle$ F
0%
AB = 4 = DE, AC = 6 = DF, $\angle$ C = $\angle$ F

Explanation

$\triangle ABC$ and

$\triangle DEF$ are congruent, then

$AB=DE$

$AC=DF$

$\angle B=\angle E$

Hence, this is the answer.

1178711_372434_ans_735f20b3eace456f90c420dea89f0f18.jpg

In the figure, AB and CD are two walls of equal height. A ladder BO is shifted to reach the other wall at D. Then, the triangles are congruent by the postulate

0%
SSS
0%
SAS
0%
ASA
0%
RHS

$\displaystyle \Delta ABC, AB=5 \ cm, BC=4 \ cm$ and

$AC=8 \ cm.$ The smallest angle is .......... and the greatest angle is ..........

0%
$\displaystyle \angle A,\angle B$
0%
$\displaystyle \angle B,\angle A$
0%
$\displaystyle \angle A,\angle C$
0%
$\displaystyle \angle B,\angle C$

Explanation

$\displaystyle \Delta ABC,$

$BC$ is the smallest side and

$AC$ is the greatest side. Hence,

$\displaystyle \angle A$ is the smallest angle and

$\displaystyle \angle B$ is the greatest angle.

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.

In the figure,

$AD$ and

$BC$ are perpendicular to

$AB$ , and

$AD=BC$ . Then , by

$SAS$ congruence postulate,

$\displaystyle \Delta ABC\cong$

0%
$\displaystyle \Delta ABD$
0%
$\displaystyle \Delta BDA$
0%
$\displaystyle \Delta BAD$
0%
$\displaystyle \Delta ADB$

Explanation

$AD\perp AB$ and

$BC\perp AB$ [ Given ]

$\therefore$

$\angle BAD=\angle ABC=90^o$ ---- ( 1 )

$\triangle ABC$ and

$\triangle BAD$

$BC=AD$ [ Given ]

$\angle ABC=\angle BAD=90^0$ [ From ( 1 ) ]

$AB=BA$ [ Common side ]

$\therefore$

$\triangle ABC\cong\triangle BAD$

1358571_378258_ans_cb212ca0e8b84df88d0ca76d5cbe5239.png

AC is a diagonal of a rectangle ABCD. Which triangle is congruent to

$\triangle$ ADC?

0%
$\triangle BCA$
0%
$\triangle ACB$
0%
$\triangle CBA$
0%
$\triangle BCD$

Explanation

$\triangle ADC$ and

$\triangle CBA$ ,

$AD=CB$ (Opposite sides of rectangle)

$DC=BA$ (Opposite sides of the rectangle)

$AC=CA$ (Common side)

$\triangle ADC\cong \triangle CBA$ by

$SSS$ criteria.

So option

$C$ is correct.

Which of the following statements is true when

$\displaystyle \Delta ABC\cong \Delta DEF.$

0%
$\displaystyle \angle A=\angle D$
0%
$\displaystyle \angle A=\angle E$
0%
$\displaystyle \angle A=\angle F$
0%
none of these

Explanation

Given $\triangle ABC \cong \triangle DEF$ .

Then the corresponding parts will also be equal.

That is by CPCT rule, corresponding parts of congruent triangles are equal.

Then, $AB=DE$ , $BC=EF$ , $AC=DF$ , $\angle A=\angle D$ , $\angle B=\angle E$ and $\angle C=\angle F$ .

Thus,

$\angle A=\angle D$ .

Hence, option

$A$ is correct.

When two triangles have corresponding sides equal in length, then the two triangles are congruent.

0%
SAS congruency Theorem
0%
AA congruency Theorem
0%
AAA congruency Theorem
0%
SSS congruency Theorem

Explanation

All

$3$ sides of a triangle are equal with all

$3$ sides of another triangle then these two triangles are said to be congruent SSS congruency Theorem.
Therefore, D is the correct answer.

Which of the following can be used to prove that

$\Delta ABC \cong \Delta SRT$ ?

0%
ASA
0%
SAS
0%
RHS
0%
AAA

Explanation

Two triangles triangle are congruent, if the hypotenuse and one side of the one triangle are respectively equal to the hypotenuse and one side of the other.
Therefore,

$\Delta ABC \cong \Delta SRT$ by RHS congruence condition.

$SAS$ congruence rule,

$\triangle PQR$ is congruent to

0%
$\triangle BCA$
0%
$\triangle CAB$
0%
$\triangle ABC$
0%
$\triangle ACB$

Explanation

$\triangle PQR$ and

$\triangle CAB,$

$PQ=CA$ [given]

$PR=CB$ [given]

and,

$\angle QPR=\angle ACB$ [given]

Thus, by

$SAS$ congruence rule,

$\triangle PQR \cong \triangle CAB$

Hence,

$Op-B$ is correct.

Which pair of triangles shows congruency by the SSS postulate?

0%
figure C
0%
figure A
0%
figure B
0%
figure D

What is the largest side of the triangle?

0%
$\overline{AB}$
0%
$\overline{BC}$
0%
$\overline{CA}$
0%
$\overline{AC}$

Explanation

$\triangle ABC,$

$\angle B$ is equal to

$90^o$ which implies that the

$\triangle ABC$ is a right-angled triangle, and in a right angle triangle side opposite to the right angle is the largest.

Because the right angle is the biggest among all three angles of the triangle.

$\Delta JKL$ and

$\Delta MNO$ ,

$\displaystyle { JL } \cong { ON }$ and

$\displaystyle { KL } \cong { OM }$ , then the condition which will make both triangles congruent is:

0%
$\displaystyle \angle L\cong \angle O$
0%
$\displaystyle \angle K\cong \angle M$
0%
$\displaystyle \angle J\cong M$
0%
$\displaystyle \angle J\cong \angle N$

Explanation

Two triangles can be congruent by the SAS test, since here we are equating two sides and one angle.

For the SAS test of congruency, the condition is that the angle must be included between the two sides to ensure correctness of the test.

Similarly, here the two included angles must be congruent for the triangles to be congruent.

They are

$\angle L \cong \angle O$ since they are the included angles of sides

$JL-KL$ and

$ON-OM$ respectively.

If three sides of a triangle are equal to three sides of another triangle, then the two triangles are congruent. This is _____ condition for congruence.

0%
$ASA$
0%
$AAS$
0%
$SSS$
0%
$SAS$

Explanation

Side-Side-Side

$(S.S.S)$ condition states that if three sides of one triangle are equal to three sides of another triangle then the two triangles are congruent.

If the hypotenuse and one of the other two sides of a right angles triangle is equal to the hypotenuse and one of the other two sides of the other right-angled triangle respectively, then the two right-angled triangles are ___.

0%
congruent
0%
unequal
0%
equilateral
0%
None of the these

$\triangle$ ABC,

$AB = 5$ cm,

$BC= 6$ cm and

$CA= 7$ cm. Identify the relation between the angles.

0%
$\angle B > \angle A > \angle C$
0%
$\angle A > \angle B > \angle C$
0%
$\angle B > \angle C > \angle A$
0%
$\angle C > \angle A > \angle B$

Explanation

In any triangle angle opposite to the longer side is larger.

Here

$CA$ is the longest side and angle opposite to it is

$\angle B$ .

$\angle B$ is largest angle.

Then comes

$BC$ and angle opposite to it is

$\angle A$

So angle

$A$ is second largest.

Then comes

$AB$ angle opposite to it is

$\angle C$

$\angle C$ is smallest.

So the decreasing order of angles is

$\angle B>\angle A>\angle C$

State true or false:

Any two right triangles with hypotenuse

$5\ cm$ , are congruent.

0%
True
0%
False

Explanation

Two triangles are congruent if their corresponding parts are equal.

Given hypotenuse of right triangle are equal but we may find a corresponding part with the right angle and the hypotenuse which may not be equal.

Hence, the statement is false.

Therefore, option

$B$ is correct.

State the following statement is True or False
Two equilateral triangles with their sides equal are always congruent

0%
False
0%
True

Explanation

Two equilateral triangle with equal sides are always congruent .

Consider two triangles

$ABC$ and

$DEF$ with sides

$AB$ and

$DE$ equal.

$AB=DE$

But because they are equilateral; other two pairs of sides are also equal.

$BC=EF$

$AC=DF$

$\therefore \triangle ABC\cong \triangle DEF$ by

$SSS$ congruency criteria.

So, the statement is true.

$\triangle ABC$ and

$\triangle DEF$ ,

$\angle B=\angle E,AB=DE,BC=EF$ . The two triangles are congruent under ............. axiom.

0%
SSS
0%
AAA
0%
SAS
0%
ASA

Explanation

Two sides and included angle of

$\triangle ABC$ and

$\triangle DEF$ are equal.

Therefore the triangles are congruent by

$SAS$ axiom.

Option

$C$ is correct.

State true or false:

Any two circles of radii

$4\ cm$ each are congruent.

0%
True
0%
False

Explanation

We know, two figures are congruent if the have same shape and size.

Then two circles are congruent if they have the same size that is their radius is equal.

Here, the radii are given to be equal, i.e.

$4cm$ Hence, the two circles are congruent.

Therefore, the statement is true and option

$A$ is correct.

Two plane figures are said to be congruent if they have_____.

0%
same size
0%
same shape
0%
same size and same shape
0%
none

Explanation

Two plane figures are congruent to each other, if trace copy of one of the figures covers the other figure completely.

Therefore, option

$C$ is correct.

State true or false:

Two equilateral triangles of side

$4\ cm$ each but labeled as

$\triangle ABC$ and

$\triangle LHN$ are not congruent.

0%
True
0%
False

State true or false:
Two circles are always congruent.

0%
True
0%
False

Explanation

We know, two figures are congruent if the have same shape and size

Then, two circles are congruent if they have the same size that is their radius is equal.

Clearly, we know, all the circles do not have the same radius.

Therefore, the statement is false.

Hence, option

$B$ is correct.

Which of the following is congruent to the above figure?

0%
0%
0%
0%
None of these

Explanation

Two figures are said to be congruent if they have exactly same shape and size or one can exactly overlap the other.

Here, if we rotate the figure in option

$C$ , and place it over each other, we get the same figure given, i.e. they will overlap.

Therefore, option

$C$ is correct.

CBSE Questions for Class 9 Maths Triangles Quiz 10 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Triangles Quiz 10 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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