7th Class Mathematics Congruence of Triangles Question Bank

done Congruence of Triangles Total Questions - 44

• question_answer1)
  In \[\Delta ABC,\] \[AB=AC\] and AD is perpendicular to BC. State the property by which \[\Delta ADB=\Delta ADC\].
  A)
  S.A.S. property done clear
  B)
  S.S.S. property done clear
  C)
  R.H.S. property   done clear
  D)
  A.S.A, property done clear
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• question_answer2)
  Two students drew a line segment each. What is the condition for them to be congruent?
  A)
   They should be drawn with a scale. done clear
  B)
   They should be drawn on the same sheet of paper. done clear
  C)
   They should have different lengths. done clear
  D)
   They should have the same length.   done clear
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• question_answer3)
  In the given figure, if \[AD=BC\] and \[AD||BC,\]which of the following is true?  
  A)
   \[AB=AD\]     done clear
  B)
        \[AB=DC\]   done clear
  C)
   \[BC=CD\]       done clear
  D)
        \[AC=AD\] done clear
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• question_answer4)
  In \[\Delta PQR\] and \[\Delta XYZ,\] \[\angle P={{50}^{o}},\] \[XY=PQ\], and \[XZ=PR\]. By which property are \[\Delta XYZ\] and \[\Delta PQR\] congruent?
  A)
   S.S.S. property done clear
  B)
   S.A.S. property   done clear
  C)
   A.S.A. property done clear
  D)
   R.H.S. property     done clear
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• question_answer5)

  A: Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other.

  R: Two triangles are congruent if two sides and the included angle of one are equal to the corresponding two sides and included angle of the other.

  Given A & R, which of the following statements is correct?
  A)
   A is false and R is the correct explanation of A.   done clear
  B)
   A is true and R is the correct explanation of A. done clear
  C)
   A is true and R is false. done clear
  D)
   A is false and R is true. done clear
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• question_answer6)
  Two triangles, A PQR and ADEF are of the same size and shape. What can we conclude about them?
  A)
   \[\Delta PQR\] is smaller than \[\Delta DFE\]. done clear
  B)
   \[\Delta PQR\] is larger than \[\Delta DFE\]. done clear
  C)
   \[\Delta PQR\] is congruent to \[\Delta DFE\].   done clear
  D)
   \[\Delta PQR\] is not congruent to \[\Delta DFE\]. done clear
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• question_answer7)
  Which of the following examines the congruence of plane figures?     
  A)
   Trial and error method done clear
  B)
   Superposition method   done clear
  C)
   Substitution method done clear
  D)
   Transposition method done clear
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• question_answer8)
  Which of the following is a pair of congruent figures?
  A)
   A regular pentagon and a regular hexagon. done clear
  B)
   A rhombus and a square. done clear
  C)
   Two equilateral triangles of the same length of their sides.   done clear
  D)
   A quadrilateral and a rectangle. done clear
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• question_answer9)
  A In \[\Delta ABC\] and \[\Delta PQR,\] \[AB=x\text{ }cm,\] \[BC=y\text{ }cm\]and \[CA=z\text{ }cm\]. What are the measures of sides PQ, QR and RP of \[\Delta PQR\] if \[\Delta ABC\cong \Delta ABC\cong \Delta PQR\]?
  A)

  PQ	QR	RP
  x cm	y cm	z cm

    done clear
  B)

  PQ	QR	RP
  y cm	x cm	z cm

  done clear
  C)

  PQ	QR	RP
  x cm	z cm	y cm

  done clear
  D)

  PQ	QR	RP
  z cm	x cm	y cm

  done clear
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• question_answer10)
  Direction: In the given figure, \[AD=CD\] and \[AB=CB\]. What are the three pairs of equal parts?
  A)
   \[\angle ADB=\angle CDB,\angle ABD=\angle CBD;\,\,BD=BD\]   done clear
  B)
   \[AD=AB,\text{ }DC=CB,\text{ }BD=BD\] done clear
  C)
   \[AB=CD,AD=BC,BD=BD\] done clear
  D)
  \[\angle ADB=\angle CDB,\angle ABD=\angle CBD;\,\,\angle DAB=\angle DBC\] done clear
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• question_answer11)
  Direction: In the given figure, \[AD=CD\] and \[AB=CB\]. Which of the following is the correct conclusion?
  A)
   \[\Delta ABC\] and \[\Delta \,CBD\] are isosceles triangles. done clear
  B)
   BD bisects \[\angle ADC\]   done clear
  C)
   BD bisects \[\angle BAD\] done clear
  D)
   \[\Delta ABC\] and \[\Delta CBD\] are equilateral triangles. done clear
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• question_answer12)
  In the given figure, \[AB=AC\] and AD is the bisector of \[\angle BAC\]. Which among the following statements is true?
  A)
          \[\Delta ADB\cong \Delta ABC\] done clear
  B)
               \[\Delta ADC\cong \Delta ABC\] done clear
  C)
               \[\angle B=\angle C\]   done clear
  D)
               \[\angle ABC=\angle CAB\] done clear
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• question_answer13)
  In \[\Delta ABC\] and \[\Delta DEF,\] \[AC=DF,AB=DE\] and \[BC=EF\]. By which property are \[\Delta ABC\] and \[\Delta DEF\] congruent?
  A)
   R.H.S. property done clear
  B)
   S.S.S. property   done clear
  C)
   S.A.S. property done clear
  D)
   A.S.A. property done clear
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• question_answer14)
  For the triangles \[\Delta ART\] and \[\Delta PEN\]given, if S.A.S. criterion should be used given \[\angle T=\angle N\] what are the respective measures of PN and RT?
  A)
   TR and PE    done clear
  B)
   AR and PEA done clear
  C)
   AT and EN      done clear
  D)
   AR and PN done clear
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• question_answer15)
  Which of the following is an example of A.S.A. criterion of congruency for two triangles \[\angle ADB\] and \[\angle DEF\]?
  A)
   \[AB=EF,\text{ }\angle B=\angle E\] and \[\angle C=\angle F\] done clear
  B)
   \[BC=EF,\text{ }\angle B=\angle E\] and \[\angle C=\angle F\]   done clear
  C)
   \[AC=EF,\text{ }\angle B=\angle D\] and \[\angle C=\angle F\] done clear
  D)
   \[AC=DE,\text{ }\angle B=\angle D\] and \[\angle C=\angle F\] done clear
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• question_answer16)
  In the figure given, \[AC=BD\] and \[\angle BAC=\angle CDB={{90}^{o}}\] If \[\Delta ABC=\Delta DCB\] by R.H.S. property which of the following is required?
  A)
   The measure of AB. done clear
  B)
   The measure of CD. done clear
  C)
   The measure of BC.   done clear
  D)
   \[AC=BD\] done clear
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• question_answer17)
  Which of the following criterion does not exist?
  A)
   A.S.A. criterion done clear
  B)
   R.H.S. criterion done clear
  C)
   A.A.A. criterion   done clear
  D)
   S.S.S. criterion done clear
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• question_answer18)
  In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?
  A)
   One triangle is an enlarged copy of other.   done clear
  B)
   The two triangles are necessarily congruent. done clear
  C)
   The two triangles are congruent by A.A.A. congruency criterion. done clear
  D)
   All of the above. done clear
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• question_answer19)

  Direction: \[\Delta ABC\] is congruent to \[\Delta PQR\] under the correspondence \[ABC\overset{{}}{\longleftrightarrow}RQP\].

  Which part corresponds to PQ?
  A)
   \[\overline{CB}\]                         done clear
  B)
   \[\overline{AC}\] done clear
  C)
   \[\overline{QR}\]                       done clear
  D)
        \[\overline{AB}\] done clear
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• question_answer20)

  Direction: \[\Delta ABC\] is congruent to \[\Delta PQR\] under the correspondence \[ABC\overset{{}}{\longleftrightarrow}RQP\].

  Which part of corresponds to RP?
  A)
  \[\overline{AB}\]                        done clear
  B)
        \[\overline{AC}\] done clear
  C)
  \[\overline{CA}\]                                    done clear
  D)
  \[\overline{BC}\] done clear
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• question_answer21)
  \[\Delta ABC\] is congruent to \[\Delta XYZ\]. Find the measures of \[\angle x\] and \[\angle y\] respectively.
  A)
         \[{{80}^{o}},{{60}^{o}}\]       done clear
  B)
          \[{{60}^{o}},{{40}^{o}}\] done clear
  C)
                   \[{{80}^{o}},{{40}^{o}}\]              done clear
  D)
          \[{{60}^{o}},{{80}^{o}}\] done clear
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• question_answer22)
  \[\Delta ABC\cong \Delta FDE\]and \[AB=3\text{ }cm,\] \[EF=8\text{ }cm\]and \[DF=10\text{ }cm\]. What are the respective lengths of AC and DE in cm?
  A)
   \[10,\,3\]                                done clear
  B)
   \[10,\,8\] done clear
  C)
    \[8,\,3\]                             done clear
  D)
          \[3,\,10\] done clear
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• question_answer23)
  \[\Delta ABC\cong \Delta FDE\] What is the measure of \[\angle F\]?
  A)
   \[{{70}^{o}}\]                          done clear
  B)
   \[{{50}^{o}}\]   done clear
  C)
   \[{{130}^{o}}\]          done clear
  D)
        \[{{60}^{o}}\] done clear
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• question_answer24)
  In the figure, \[PQ\text{ =}PS\] and \[QR=SR\]. If \[\Delta PQR\] is congruent to \[\Delta PSR,\] which of the following is correct?
  A)
         \[\angle QPR=\angle PRS\] done clear
  B)
                   \[\angle RPS=\angle RQP\] done clear
  C)
                   \[\angle QRP=\angle SRP\]   done clear
  D)
                   \[\overline{PR}=\overline{RS}\] done clear
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• question_answer25)
  AB and AC are two chords of a circle with centre O as shown. If \[\Delta AOB\] is congruent to \[\Delta AOC,\] which of the following is correct?
  A)
   \[\angle OBA=\angle OCA\]   done clear
  B)
   \[\angle AOC=\angle OCA\] done clear
  C)
   \[AO=AC\] done clear
  D)
   \[AB=OC\] done clear
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• question_answer26)
  A regular hexagon is divided into four triangles. Which of the following is correct?
  A)
   \[\Delta ABF\cong \Delta EDF\]   done clear
  B)
   \[\Delta FDC\cong \Delta FCB\] done clear
  C)
   \[\Delta ABF\cong \Delta FBC\] done clear
  D)
   \[\Delta FDC\cong \Delta BCF\] done clear
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• question_answer27)
  \[\Delta ABC\] and \[\Delta DEF\] are as shown. By which condition of congruence is\[\Delta ABC\cong \Delta DEF\]?
  A)
   S.S.S. condition done clear
  B)
   S.A.S. condition done clear
  C)
   R.H.S. condition   done clear
  D)
   A.S.A. condition. done clear
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• question_answer28)
  Given \[AB||CD\] and AB = CD, which of the following is correct?            
  A)
               \[\Delta AOB\cong \Delta DOC\]   done clear
  B)
                   \[\Delta AOB\cong \Delta ODC\] done clear
  C)
                   \[\Delta BOA\cong \Delta DOC\] done clear
  D)
                   \[\Delta BAO\cong \Delta COD\] done clear
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• question_answer29)
  \[\Delta ABC\] is isosceles, \[AB=AC\] and \[AD\bot BC,\] Which of the following is correct? 
  A)
   \[\Delta ADC\cong \Delta ADB\]   done clear
  B)
   \[\Delta ADB\cancel{\cong }\Delta ADB\] done clear
  C)
   \[\Delta ADB\cong \Delta ABC\] done clear
  D)
   \[\Delta ABC\cong \Delta ADC\] done clear
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• question_answer30)
  Observe the triangles given in the figure. State the condition under which \[\Delta ABC\cong \Delta PQR\]
  A)
   A.S.A.              done clear
  B)
        S.S.S.   done clear
  C)
   S.A.S.              done clear
  D)
        R.H.S. done clear
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• question_answer31)
   In the given figure, \[AB=AC\] and \[AD=AE\]. Which of the following statements is not true?
  A)
   \[\angle CAE=\angle BAD\] done clear
  B)
   \[\Delta ACE=\Delta ABD\] done clear
  C)
   \[\Delta AEC=\Delta ABD\]   done clear
  D)
   \[BE=DC\] done clear
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• question_answer32)
  ABCD is a parallelogram in which  \[AB=DC\] and \[AD=BC\]. By which condition of congruence of triangles is\[\Delta ABD\cong \Delta CDB\]?
  A)
   R.H.S.              done clear
  B)
        S.A.S. done clear
  C)
   S.S.S.                done clear
  D)
        A.S.A. done clear
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• question_answer33)
  Given \[\Delta XYZ\] and \[\Delta LMN.\] Choose the correct statement.
  A)
   \[\Delta XYZ\cong \Delta LMN\]   done clear
  B)
   \[YZ=LM\] done clear
  C)
   \[XY=MN\]        done clear
  D)
   \[XZ=LM\] done clear
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• question_answer34)
  Identify the incorrect statement.
  A)
   The corresponding sides of congruent triangles are equal. done clear
  B)
   The corresponding angles of congruent triangles are equal. done clear
  C)
   Two triangles cannot be congruent.   done clear
  D)
   There are four congruency conditions for congruence of triangles. done clear
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• question_answer35)
  A By which congruency property are the two triangles PQS and PRS given in the following figure congruent?
  A)
   S.S.S. property done clear
  B)
   S.A.S. property   done clear
  C)
   A.S.A. property done clear
  D)
   R.H.S. property done clear
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• question_answer36)
  In the following figure, two triangles ABC and EDC are such that \[AC=EC,\text{ }BC=DC,\] \[\angle E={{60}^{o}},\] \[\angle DCE={{30}^{o}},\] and \[\angle B={{90}^{o}},\]. By which property is \[\Delta ABC\cong \Delta EDC\]?
  A)
   S.S.S. property done clear
  B)
   S.A.S. property done clear
  C)
   A.S.A. property done clear
  D)
   R.H.S. property   done clear
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• question_answer37)
  For the congruence of \[\Delta ABC\] and \[\Delta PQR,\] which one of the following sets of conditions is not sufficient?
  A)
                \[\angle ABC=\angle PQR,\] \[a=p,\,\,c=r\] done clear
  B)
               \[\angle CAB=\angle RPQ,\angle ABC=\angle PQR,c=r\] done clear
  C)
               \[b=q,\,\,\angle CAB=\angle RPQ,\,\,a=p\]   done clear
  D)
               \[a=p,\,c=r,\,\angle ABC=\angle PQR\] done clear
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• question_answer38)
  Which of the following are congruent?
  A)
   Two Rs. 1 coins   done clear
  B)
   A Rs. 1 coin and a Rs. 2 coin done clear
  C)
   A Rs. 2 coin and a Rs. 5 coin done clear
  D)
   A Rs. 5 coin and a Rs. 10 coin done clear
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• question_answer39)
  Which of the following is important in congruence of triangles?
  A)
   Naming the angles of the triangles using capital letters. done clear
  B)
   Measures of angles in degrees. done clear
  C)
   The order of letters of the triangles.   done clear
  D)
   Exact length of the sides of the triangles. done clear
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• question_answer40)
  In the figure given, which of the following statements is true?
  A)
               \[\Delta QPR\cong \Delta SPR\]   done clear
  B)
                          \[\Delta PSR\cong \Delta RQP\] done clear
  C)
                   \[\Delta PRS\cong \Delta QPR\] done clear
  D)
                   \[\Delta QRP\cong \Delta PSR\] done clear
  View Solution play_arrow

• question_answer41)
  In two triangles, pairs of corresponding sides and the corres-ponding angles are equal. What can be concluded from this?
  A)
   The triangles are small. done clear
  B)
   The triangles are congruent.   done clear
  C)
   The triangles are equilateral. done clear
  D)
   The triangles are equiangular. done clear
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• question_answer42)
  Which of the following are measurements of two triangles by which they are congruent under S.A.S condition?
  A)
   \[\Delta ABC:\angle B={{50}^{o}},BC=5cm,\] and \[AB=7cm.\] \[\Delta DEF:\angle E={{50}^{0}},EF=7cm,\]and\[DE=5cm.\]   done clear
  B)
   \[\Delta ABC:BC=6cm,\] \[AC=4\,\,cm\] and \[\angle B={{35}^{o}}\] \[\Delta DEF:DF=4\,cm,\] \[EF=6\,cm\] and \[\angle D={{55}^{o}}\] done clear
  C)
  \[\Delta ABC:AB=4.5cm,\]\[AC=4cm\]and\[\angle A={{60}^{o}}\] \[\Delta DEF:DE=4cm,FD=4.5cm\]and\[\angle D={{55}^{o}}\] done clear
  D)
   Either [b] or [c] done clear
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• question_answer43)
  \[\Delta ABC\] is isosceles with \[AB=AC,\] \[AD\bot BC;\] which of the following is a correct statement?
  A)
               \[\Delta ABC\cong \Delta ADC\] done clear
  B)
               \[\Delta ABD\cong \Delta ACD\]   done clear
  C)
               \[\Delta ADB\cong \Delta ACD\] done clear
  D)
               \[\Delta ADC\cong \Delta ABD\] done clear
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• question_answer44)
  Are triangles in the given figure congruent by R.H.S. condition?
  A)
   Yes          done clear
  B)
     Insufficient data done clear
  C)
   No           done clear
  D)
   Either [b] or [c] done clear
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