CBSE Questions for Class 7 Maths Congruence Of Triangles Quiz 1 - MCQExams.com

Given that $$\Delta ABC = \Delta FDE$$ and $$AB = 5 cm, \angle B = 40^{0}$$ and $$\angle A = 80^{0}$$ then which of the following relation is true?
  • $$DF=5cm,\angle F=60^{0}$$
  • $$DF=5cm,\angle E=60^{0}$$
  • $$DE=5cm,\angle E=60^{0}$$
  • $$DE=5cm,\angle D=40^{0}$$
ABC is an isosceles triangle with AB $$= $$AC and D is a point on BC such that  $$AD \perp BC$$ (Fig. 7.13). To prove that $$\angle BAD = \angle CAD,$$ a student proceeded as follows:

$$\Delta ABD$$ and $$ \Delta ACD,$$
AB $$=$$ AC (Given)
$$\angle B = \angle C$$   (because AB $$=$$ AC)
and $$\angle ADB = \angle ADC$$
Therefore, $$\Delta ABD \cong \Delta ACD (AAS)$$
So, $$\angle  BAD = \angle CAD (CPCT)$$
What is the defect in the above arguments?

78853_330861415ee64345b8ba219aaf8ae2ec.png
  • It is defective to use $$\angle ABD = \angle ACD$$ for proving this result.
  • It is defective to use $$\angle ADB = \angle ADC$$ for proving this result.
  • It is defective to use $$\angle BAD = \angle DCA$$ for proving this result.
  • Cannot be determined
Given $$\Delta OAP \cong  \Delta OBP$$ in figure, the criteria by which the triangles are congruent is:

85097_33d8e236f4ec4665aa7c0a2a618fd736.png
  • $$SAS$$
  • $$SSS$$
  • $$RHS$$
  • $$ASA$$
If $$\Delta ABC \cong  \Delta DEF$$ by SSS congruence rule then
  • $$AB=EF,BC=FD,CA=DE$$
  • $$AB=FD,BC=DE,CA=EF$$
  • $$AB=DE,BC=EF,CA=FD$$
  • $$AB=DE,BC=EF,\angle C = \angle F$$
In $$\Delta ABC$$ and $$\Delta DEF$$, AB = DF and $$\angle A = \angle D$$. The two triangles will be congruent by SAS axiom if :
  • BC = EF
  • AC = DE
  • BC = DE
  • AC = EF
In triangles ABC and DEF, AB $$=$$ FD and $$\angle A = \angle D$$. The two triangles will be congruent by
SAS axiom if :
  • BC $$=$$ EF
  • AC $$=$$ DE
  • AC $$=$$ EF
  • BC $$=$$ DE
In $$\Delta ABC$$ and $$\Delta DEF$$, $$AB=FD$$, $$\angle A= \angle D$$. The two triangles will be congruent by SAS axiom if :
  • $$BC=DE$$
  • $$AC=EF$$
  • $$BC=EF$$
  • $$AC=DE$$
In the given figure, If OA=OB,OD=OC, then $$\Delta AOD \cong \Delta BOC$$ by congruence rule:

87720_3f69271d5d13425f9e48040978676e71.png
  • SSS
  • ASA
  • SAS
  • RHS
If $$\Delta ABC \cong \Delta DEF$$ by SSS congruence rule then :
  • $$AB=EF, BC=FD, CA=DE$$
  • $$AB=FD, BC=DE, CA=EF$$
  • $$AB=DE, BC=EF, CA=FD$$
  • $$AB=DE, BC=EF, \angle C=\angle F$$
In the given figure, if $$AB=DC$$, $$\angle ABD= \angle CDB$$, which congruence rule would you apply to prove $$\Delta ABD$$ $$\cong \Delta CDB$$ ?
86849_c6c45dd2a7b6431ca525ca81561d0188.png
  • SAS
  • ASA
  • RHS
  • SSS
State true or false:
If two sides and an angle of a triangle are respectively equal to two sides and an angle of another triangle,then the two triangles are always congruent. 
  • True
  • False

By which congruency are the following pairs of triangles congruent:

In $$\Delta\,ABC$$ and $$\Delta PQR$$, $$AB=PQ$$, $$BC=QR$$ and $$AC=PR$$
  •  $$ASA$$
  •  $$SSS$$
  •  $$AAA$$
  • $$ASS$$
Angles opposite to the equal sides of a triangle are equal. 
  • True
  • False
  • Incomplete information
  • None

State true/false:

If in $$\Delta\, ABC$$ and $$\Delta \,DEF$$, AB = DE, BC = DE, BC = EF and $$\angle\,B\,=\, \angle\,E$$, then both the triangles are congruent.
  • True
  • False
In a triangle $$ABC$$ and $$DEF$$, $$AB=FD$$ and $$\angle A=\angle D$$. The two triangles will be congruent by SAS axiom if:
242665.png
  • $$BC=EF$$
  • $$AC=DE$$
  • $$AC=EF$$
  • $$BC=DE$$
If in two triangles $$ABC$$ and $$PQR$$, $$AB=\, QR$$, $$\angle A=\angle Q$$ and $$\angle B=\angle R$$, then $$\triangle ABC\cong$$ $$\triangle $$ 
  • $$QRP$$
  • $$PQR$$
  • $$PRQ$$
  • None of the above.
If in two triangles $$ABC$$ and $$DEF$$, $$AB=\,DF$$, $$BC=\,DE$$ and $$\angle B=\angle D$$, then $$\triangle ABC\cong $$ $$\triangle $$____.
  • $$FDE$$
  • $$DEF$$
  • $$EDF$$
  • $$EFD$$
If the two sides and the ____ angle of one triangle are respectively equal to two sides and the included angle of the other triangle, then the triangles are congruent.
  • Included
  • Excluded
  • Adjacent
  • Any
Which of the following pairs of triangles are congruent?
  • $$\triangle ABC$$ and $$\triangle DEF$$ in which : $$BC=\,EF$$, $$AC=\,DF$$ and $$\angle C=\angle F$$
  • $$\triangle ABC$$ and $$\triangle DEF$$ in which : $$AB=\,PQ$$, $$BC=\,QR$$ and $$\angle C=\angle R$$
  • $$\triangle ABC$$ and $$\triangle LMN$$ in which : $$\angle A=\angle L={ 90 }^{ 0 }$$, $$AB=\,LM$$, $$\angle C={ 40 }^{ 0 }$$ and $$\angle M={ 50 }^{ 0 }$$
  • $$\triangle ABC$$ and $$\triangle DEF$$ in which : and $$\angle B=\angle E={ 50 }^{ 0 }$$ and $$AC=\,DF$$
If ____sides of a triangle are respectively equal to the ____ sides of the other triangle, then the triangles are congruent.
  • Three
  • Two
  • One
  • None
Which of the following statements is true when $$\displaystyle \Delta ABC\cong \Delta DEF.$$
  • $$\displaystyle \angle A=\angle D$$
  • $$\displaystyle \angle A=\angle E$$
  • $$\displaystyle \angle A=\angle F$$
  • none of these
When two triangles have corresponding sides equal in length, then the two triangles are congruent.
  • SAS congruency Theorem
  • AA congruency Theorem
  • AAA congruency Theorem
  • SSS congruency Theorem
In $$\Delta ABC$$, AB = AC and AD is perpendicular to BC. State the property by which $$\Delta ADB\, \cong\, \Delta ADC$$.
  • SAS property
  • SSS property
  • RHS property
  • ASA property
In the following fig. if $$AB=AC$$ and $$BD= DC$$ then $${\angle ADC}$$ =
265572_4d065936bff244cf8d76d2608d8a1aee.png
  • $${60^ 0}$$
  • $${120^ 0}$$
  • $${90^ 0}$$
  • None
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
378257.PNG
  • SSS
  • SAS
  • ASA
  • RHS
State the property by which$${\triangle }$$ADB   $${\cong }$$  $${\triangle }$$ADC in the following figure.
265566_d263e9f67c664d2e9f72dc1a0e74ff1d.png
  • SAS property
  • SSS property
  • RHS property
  • ASA property
In the figure, $$\displaystyle AB=CD$$ and $$\displaystyle \angle A={ 90 }^{ o }=\angle D$$. Then 

377041.PNG
  • $$\displaystyle \Delta ABC\cong \Delta DBC$$ by SAS postulate
  • $$\displaystyle \Delta ABC\cong \Delta DCB$$ by RHS postulate
  • $$\displaystyle \Delta ABC\cong \Delta DBC$$ by AAS postulate
  • $$\displaystyle \Delta ABC\cong \Delta DCB$$ by SSS postulate
In the figure, $$AD$$ and $$BC$$ are perpendicular to $$AB$$, and $$AD=BC$$. Then , by $$SAS$$ congruence postulate, $$\displaystyle \Delta ABC\cong $$
378258_f2321200e5154b78adcdff51ea8ce88c.png
  • $$\displaystyle \Delta ABD$$
  • $$\displaystyle \Delta BDA$$
  • $$\displaystyle \Delta BAD$$
  • $$\displaystyle \Delta ADB$$
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.
  • $$ASA$$
  • $$AAS$$
  • $$SSS$$
  • $$SAS$$
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 ___.
  • congruent
  • unequal
  • equilateral
  • None of the these
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