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CBSE Questions for Class 7 Maths Congruence Of Triangles Quiz 2 - MCQExams.com
CBSE
Class 7 Maths
Congruence Of Triangles
Quiz 2
AC is a diagonal of a rectangle ABCD. Which triangle is congruent to $$\triangle$$ ADC?
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$$\triangle BCA$$
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$$\triangle ACB$$
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$$\triangle CBA$$
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$$\triangle BCD$$
Explanation
In $$\triangle ADC$$ 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 can be used to prove that $$\Delta ABC \cong \Delta SRT$$?
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ASA
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SAS
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RHS
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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.
State true or false:
Any two right triangles with hypotenuse $$5\ cm$$, are congruent.
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True
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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.
By $$SAS$$ congruence rule, $$\triangle PQR$$ is congruent to
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$$\triangle BCA$$
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$$\triangle CAB$$
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$$\triangle ABC$$
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$$\triangle ACB$$
Explanation
In $$\triangle PQR$$ 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?
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figure C
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figure A
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figure B
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figure D
Explanation
From figure C, triangles are congruent by the SSS postulate because the three sides of one triangle are congruent to three sides of another triangle.
Therefore, the given triangles are congruent by the SSS congruency postulate.
In $$\Delta JKL$$ and $$\Delta MNO$$, $$\displaystyle { JL } \cong { ON } $$ and $$\displaystyle { KL } \cong { OM } $$, then the condition which will make both triangles congruent is:
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$$\displaystyle \angle L\cong \angle O$$
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$$\displaystyle \angle K\cong \angle M$$
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$$\displaystyle \angle J\cong M$$
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$$\displaystyle \angle J\cong \angle N$$
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.
Which of the following is congruent to the above figure?
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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 $$A$$, and place it over each other, we get the same figure given, i.e. they will overlap.
Therefore, option $$A$$ is correct.
State the following statement is True or False
Two equilateral triangles with their sides equal are always congruent
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True
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False
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.
In $$\triangle ABC$$ and $$\triangle DEF$$, $$\angle B=\angle E,AB=DE,BC=EF$$. The two triangles are congruent under ............. axiom.
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SSS
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AAA
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SAS
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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.
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True
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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_____.
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same size
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same shape
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same size and same shape
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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.
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True
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False
Explanation
Two equilateral triangles with equal sides are always congruent no matter how they are labeled.
So the statement is False.
State true or false:
Two circles are always congruent.
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True
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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.
In the given figure, $$PA$$ $$\perp$$ $$AB$$, $$QB$$ $$\perp$$ $$AB$$ and $$\Delta$$ $$OAP$$ $$\cong \Delta$$ $$OBQ$$, then:
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$$PA$$ $$=$$ $$OB$$
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$$AP$$ $$=$$ $$QB$$
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$$OP$$ $$=$$ $$BQ$$
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$$OA$$ $$=$$ $$OQ$$
Explanation
It is given that
$$\Delta OAP $$ $$\cong $$ $$\Delta OBQ$$ both triangles are congruent.
That is by CPCT rule, corresponding parts of congruent triangles are equal.
Then,
$$OA = OQ , AP = QB , OP = OQ$$
, $$\angle O=\angle O$$, $$\angle A=\angle B$$ and $$\angle P=\angle Q$$.
So, option $$B$$ is correct.
If for $$\triangle$$ABC and $$\triangle$$DEF, the correspondence CAB $$\leftrightarrow$$ EDF gives a congruence, then which of the following is NOT true?
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AC = DE
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AB = EF
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$$\angle$$A = $$\angle$$D
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$$\angle$$C = $$\angle$$E
Explanation
In $$\triangle ABC$$ and $$\triangle DEF$$
$$\Rightarrow$$ The correspondence $$CAB\leftrightarrow EDF$$ gives a congruence.
$$\Rightarrow$$ So, $$CA=ED,\,AB=DF,\,CB=EF$$
$$\Rightarrow$$ $$\angle CAB=\angle EDF,\,\angle ACB=\angle DEF,\,\angle ABC=\angle DFE$$
$$\therefore$$ $$AB=EF$$ is not true.
Which of the following is congruent to the above figure?
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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.
In $$\triangle ABC$$, if $$AB = 7$$ cm, $$\angle A= 40^o$$ and $$\angle B = 70^o$$, which criterion can be used to construct this triangle?
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ASA
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SSS
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SAS
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RHS
Explanation
Given : In a triangle $$ABC, AB = 7 cm, \angle A=40^{o}$$ and $$\angle B=70^{o}$$
So, here we know two of the angles and a side including these angles.
Hence, Angle Side Angle i.e ASA criterion can be used to construct this triangle.
706o
Which of the following pair of triangles are congruent by RHS criterion?
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(i) and (ii)
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(iii) and (iv)
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(i) and (iii)
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(ii) and (iv)
Explanation
In $$\triangle ABC$$ and $$\triangle QRP$$
$$\Rightarrow$$ $$AB=QR=4\,cm$$
$$\Rightarrow$$ $$BC=RP=5\,cm$$ [Hypotenuse]
$$\Rightarrow$$ $$\angle A=\angle Q=90^o$$
$$\therefore$$ $$\triangle ABC\cong\triangle QRP$$ [By RHS criteria]
Which of the following is congruent to the above figure?
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0%
0%
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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 $$B$$, and place it over each other, we get the same figure given, i.e. they will overlap.
Therefore, option $$B$$ is correct.
Direction (14 - 15) : Study the figure and information given below carefully and answer the following questions.
CF and AE are equal perpendiculars on BD, BF = FE = ED.
$$\triangle$$ABE is congruent to
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$$\triangle$$AED
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$$\triangle$$BFC
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$$\triangle$$CDF
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$$\triangle$$BCD
Explanation
In $$\triangle ABE$$ and $$\triangle CDF$$
$$\Rightarrow$$
$$AE = CF$$
[given]
$$\Rightarrow$$ $$\angle AEB=\angle CFD$$ [given]
$$\Rightarrow$$
$$BF + FE = DE + EF$$
$$\Rightarrow$$
$$BE = DF$$
$$\therefore$$ $$ \triangle ABE \cong \triangle CDF$$ [By SAS criteria]
By which congruency criterion, $$\triangle$$PQR $$\cong$$ $$\triangle$$PQS?
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RHS
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ASA
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SSS
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SAS
Explanation
In $$\triangle PQR$$ and $$\triangle PQS$$
$$\Rightarrow$$ $$PR = PS = a \,cm$$ [given]
$$\Rightarrow$$ $$RQ = SQ = b\,cm $$ [given]
$$\Rightarrow$$ $$PQ = PQ$$ [common side]
$$\Rightarrow$$
$$\triangle PQR \cong \triangle PQS$$ (By SSS)
In the given figure, triangles $$ABC$$ and $$DCB$$ are right angled at $$A$$ and $$D$$ respectively and $$AC$$ $$=$$ $$DB$$, then $$\Delta$$ $$ABC$$ $$\cong\Delta$$ $$DCB$$ of from.
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$$AAA$$
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$$SAS$$
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$$RHS$$
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None of these
Explanation
In
$$\Delta ABC$$ and
$$\Delta DCB,$$
$$AC = DB$$ [Given]
$$ \angle BAC = \angle CDB = 90^{\circ}$$
$$BC=BC$$ [Common Hypotenuse ]
So, by $$RHS$$ rule of congruence,
$$\Delta ABC $$ $$\cong $$ $$\Delta DCB$$
Hence, option
$$C$$ is correct.
The ________ criterion is used to construct a triangle congruent to another triangle whose length of three sides are given.
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$$SAS$$
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$$SSS$$
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$$RHS$$
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$$ASA$$
Explanation
When the length of all three sides of a triangle are given, then by Side-Side-Side i.e. $$SSS$$ criterion we can say that the sides of the other triangle will be equal to that by $$CPCT$$.
Hence, the answer is $$SSS$$.
State True or False. If false, give reasons for that:
If two triangles are congruent, their corresponding angle are equal.
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True
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False
Explanation
If two triangles are congruent, then we know, their corresponding parts are equal. This rule is known as CPCT rule. That is, their corresponding angles and corresponding sides are equal.
Therefore, by CPCT rule, we can say that if two triangle are congruent then their corresponding angles are equal.
Hence the given statement is true.
Therefore, option $$A$$ is correct.
State True or False. If false, give reasons:
A 1-rupee and a 5-rupee coins are congruent.
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True
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False
Explanation
We know, two shapes are congruent, if they have the same shape and size.
Consider a $$1-rupee$$ coin and
a $$5-rupee$$ coin.
Both the coins are in the shape of a circle.
But considering the size,
$$5-rupee$$ coin is thicker than
$$1-rupee$$ coin.
Hence, the given statement is false.
Therefore, option B is correct.
If $$ \triangle ABC$$ and $$\triangle DBC$$ are on the same base BC,AB=DC and AC=DB,then which of the following gives a CORRECT congruence relationship?
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$$\triangle ABC=\triangle DBC$$
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$$\triangle ABC=\triangle CBD$$
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$$\triangle ABC=\triangle DCB$$
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$$\triangle ABC=\triangle BCD$$
Explanation
In triangle $$\Delta ABC$$ and $$\Delta DCB$$ we have
$$AB=DC$$ , $$AC=DB$$ and $$BC=BC$$
then from $$SSS$$ congruence ,$$\Delta ABC=\Delta DCB$$
Which of the following triangles is congruent to the given triangle?
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0%
0%
0%
Explanation
Triangle in option (C) is congruent to given triangle by SAS congruene criteria.
Two triangles are congruent, if two angles and the side included between them in one triangle is equal to the two angles and the side included between them of the other triangle.This is known as
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RHS congruence criterion
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ASA congruence criterion
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SAS congruence criterion
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SSS congruence criterion
Explanation
When two angles and side included in between these angles of one triangle are same as another one, both these triangle are Congruent.
This criteria of congruency is knows as ASA criterion as a side included between two angles are all same.
$$\textbf{Hence the answer is option (b)}$$
Which pair of triangles is not congruent by $$SAS$$ congruence criterion
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None of these
Explanation
In option (3), we have
$$\angle BAC = \angle DFE = 120^{\circ}$$
$$BC = DE = 5$$
$$AC = DF = 3$$
For SAS to hold true corresponding angle included by two congruent sides must be congruent
here, angle A and F have not included angles by the congruent sides.
Hence, $$\triangle ABC \not\cong \triangle DEF$$
State True or False:
In $$\triangle ABC$$ and $$\triangle PQR$$, $$AB=PQ,BC=QR$$ and $$CB$$ and $$RQ$$ are extended to $$X$$ and $$Y$$ respectively and $$\angle ABX=\angle PQY$$ then $$\triangle ABC \cong \triangle PQR$$.
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True
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False
Explanation
From the above figure we can conclude that,
$$\angle ABX+\angle ABC = 180^o\quad\quad\dots(1)$$
$$\angle PQY+\angle PQR = 180^o\quad\quad\dots(2)$$
But it is given that,
$$\angle ABX =\angle PQY\quad\quad\dots(3)$$
From $$(1),\ (2),$$ and $$(3)$$ we can conclude that,
$$\angle ABC = \angle PQR$$
Now, in $$\triangle ABC$$ and $$\triangle PQR,$$
$$AB=PQ$$ [Given]
$$\angle ABC = \angle PQR$$
$$BC=QR$$ [Given]
So, by $$SAS$$ rule of congruence,
$$\triangle ABC\cong\triangle PQR$$
Hence, the given statement is true.
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