7th Class Mental Ability Congruence of Triangles Question Bank

done Congruence of Triangles Total Questions - 39

• question_answer1)
  In the given figures, \[\Delta DEF\cong \Delta KJI.\] What is the measure of\[\overline{FD}?\]
  A)
  \[\overline{JI}\]                                    done clear
  B)
  \[\overline{KJ}\]                      done clear
  C)
       \[\overline{EF}\]                      done clear
  D)
       \[\overline{KI}\] done clear
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• question_answer2)
  If\[\Delta ABC=\Delta LMN,\]identify the angle that corresponds to\[\angle A.\]
  A)
   \[\angle L\] done clear
  B)
   \[\angle B\] done clear
  C)
   \[\angle N\] done clear
  D)
   \[\angle M\] done clear
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• question_answer3)
  From the given figure, which of the following is correct?
  A)
  \[\Delta PQR\cong \Delta PQS\]          done clear
  B)
  \[\Delta PQR\cong \Delta QPS\] done clear
  C)
       \[\Delta PQR\cong \Delta SQP\] done clear
  D)
       \[\Delta PQR\cong \Delta SPQ\] done clear
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• question_answer4)
  By which congruence rule are the two triangles in the given figure congruent?
  A)
   R.H.S             done clear
  B)
   S.A.S  done clear
  C)
        A.S.A  done clear
  D)
        S.S.S done clear
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• question_answer5)
  \[\Delta BDC\cong \Delta MLK.\] Which of the following is correct?
  A)
  \[DB=MK;\,\angle D=\angle M,\angle C=LK\] done clear
  B)
  \[BC=MK;\,\angle D=\angle L,DC=LK\] done clear
  C)
  \[\angle A=\angle M;BD=ML;\angle C=\angle L\] done clear
  D)
  \[DB=MK;DC=\angle K;\angle B=ML\] done clear
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• question_answer6)
  By which congruency condition are the two triangles in the given figure congruent?
  A)
   S.S.S.             done clear
  B)
   R.H.S done clear
  C)
                    S.A.S  done clear
  D)
                    A.S.A done clear
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• question_answer7)
  If \[\Delta KLM\]and\[\Delta OPQ\]are equilateral triangles and KL = OP, find the condition under which \[\Delta KLM\cong \Delta OPQ.\]
  A)
   A.S.A.             done clear
  B)
   R.H.S done clear
  C)
        S.S.S. done clear
  D)
        S.A.S. done clear
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• question_answer8)
  \[\Delta ABC\cong \Delta DFE\]by S.A.S. congruence criterion, Which one of the following is not a matching part?
  A)
   AB = DF                    done clear
  B)
  \[\angle ABC=\angle DFE\]                 done clear
  C)
   AC = DE        done clear
  D)
        BC = DE done clear
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• question_answer9)
  In the given figure, \[\Delta UVW\cong \Delta XYW\](by S.A.S. rule.) What is the value ?m??
  A)
  \[15{}^\circ \]                  done clear
  B)
  \[20{}^\circ \] done clear
  C)
  \[30{}^\circ \] done clear
  D)
  \[40{}^\circ \] done clear
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• question_answer10)
  In the figure, AE = AD. Which additional piece of information (matching part) is needed to prove \[\Delta AEF\cong \Delta ADB\]by A.S.A.?
  A)
  \[\angle ABD=\angle ACE\]     done clear
  B)
  \[\angle AEC=\angle ADB\] done clear
  C)
        BD = CE        done clear
  D)
        AB = AC done clear
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• question_answer11)
  In congruence triangles KLM and XYZ, three equality relations between some corresponding parts are \[KL=YX,\angle L=\angle Y\]and\[\angle M=\angle Z.\] By which congruence condition are the triangles congruent?
  A)
   R.H.S.                        done clear
  B)
   S.S.S.             done clear
  C)
   S.A.S.             done clear
  D)
        A.S.A. done clear
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• question_answer12)
  In the given isosceles \[\Delta ABC, AB=AC. AD\bot BC.\] By which congruence condition\[\Delta ABD\cong \Delta ACD?\]
  A)
   S.S.S.                         done clear
  B)
   R.H.S.            done clear
  C)
  S.A.S.             done clear
  D)
   A.S.A. done clear
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• question_answer13)
  Identify the correct words that fill the blank. Two circles with equal radii are____.
  A)
   congruent                    done clear
  B)
   not congruent              done clear
  C)
   not similar         done clear
  D)
                    similar done clear
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• question_answer14)
  If\[\Delta PQR\cong \Delta XYZ,\]find the value of m.
  A)
  \[7{}^\circ \]                       done clear
  B)
  \[96{}^\circ \] done clear
  C)
  \[100{}^\circ \] done clear
  D)
  \[60{}^\circ \] done clear
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• question_answer15)
  Consider the following statements. (i) Equality of two sides of one triangle with any two sides of the second makes the triangle congruent. (ii) Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangles congruent.                   (iii) Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangle congruent. Which of the statement are correct?
  A)
   (i), (ii) and (iii) are correct done clear
  B)
   (i) and (ii) are correct done clear
  C)
   (i) and (ii) done clear
  D)
   (ii) and (iii) done clear
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• question_answer16)
  By which congruency criteria are the two triangles in the given figure congruent?
  A)
   S.A.S.                         done clear
  B)
   R.H.S. done clear
  C)
        A.S.A. done clear
  D)
        S.S.S. done clear
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• question_answer17)
  In the adjacent figure,\[\overline{DA}\bot \overline{AB},\overline{CB}\bot \overline{AB}\]and AC = BD. Which of the following statements is true?
  A)
  \[\Delta ABC\cong \Delta BAD\]          done clear
  B)
  \[\Delta ABC\cong \Delta ABD\]          done clear
  C)
  \[\Delta ABC\equiv /\Delta BAD\] done clear
  D)
       \[\Delta ABC\ne \Delta ABD\] done clear
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• question_answer18)
  In the figure, \[\Delta ABC\]is similar to \[\Delta XYZ,AB=4\,cm,XY=6cm,\]\[YZ=5\,cm\]and \[\angle XYZ={{113}^{o}}.\]Find\[\angle ABC\]and the length of BC.
  A)
  \[{{113}^{o}},2\frac{1}{3}\]                     done clear
  B)
  \[{{113}^{o}},3\frac{1}{3}\]         done clear
  C)
  \[{{113}^{o}},4\frac{1}{3}\]         done clear
  D)
  \[{{113}^{o}},5\frac{1}{3}\] done clear
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• question_answer19)
  In the diagram, \[\Delta ABC\]is congruent to \[\Delta PQR.\]Find the respective values of\[\angle x\]and \[\angle y.\]
  A)
  \[{{80}^{o}},{{50}^{o}}\]                       done clear
  B)
  \[{{70}^{o}},{{50}^{o}}\]           done clear
  C)
  \[{{80}^{o}},{{60}^{o}}\]           done clear
  D)
   \[{{70}^{o}},{{40}^{o}}\]           done clear
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• question_answer20)
  In the figure, given that AB = CF, EF = BD and \[\angle AFE=\angle DBC,\]by which congruence is\[\Delta AFE\cong \Delta CBD?\]
  A)
   S.S.S. done clear
  B)
   S.A.S. done clear
  C)
   A.S.A. done clear
  D)
   R.H.S. done clear
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• question_answer21)
  In the following figure, \[\angle DAC={{30}^{o}},\angle ABC=\angle ADC={{95}^{o}}\]and \[\angle BCA={{55}^{o}}.\]if the area of \[\Delta ACD\]is \[30\,sq.\,cm,\]what is the area of \[\Delta ABC?\]
  A)
   30 sq. cm                    done clear
  B)
   15 sq. cm                    done clear
  C)
   45 sq. cm        done clear
  D)
  60 sq. cm done clear
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• question_answer22)
  In the given figure \[\overline{BC}||\overline{EF},BC=EF\]and \[DF=AC.\]which of the following congruency axiom (s) is/are suitable to prove that \[\Delta BCA\cong \Delta EFD?\]
  A)
   S.S.S.                         done clear
  B)
   S.A.S. done clear
  C)
   R.H.S.              done clear
  D)
  All of these done clear
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• question_answer23)
  Vani wants to prove that \[\Delta FGH\cong \Delta JKL\]using R.H.S. congruency rule. She knows that FG = JK and FH = JL. What additional piece of information does she need?
  A)
  \[\angle H=\angle K={{90}^{o}}\]         done clear
  B)
  \[\angle F=\angle G={{90}^{o}}\] done clear
  C)
                   \[\angle G=\angle K={{90}^{o}}\]  done clear
  D)
         \[\angle F=\angle J={{90}^{o}}\]   done clear
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• question_answer24)
  If \[\Delta NKL\cong \Delta LMN,\]find the value of \[x.\]
  A)
  \[45{}^\circ ~\] done clear
  B)
  \[32{}^\circ ~\] done clear
  C)
  \[48{}^\circ ~\] done clear
  D)
  \[60{}^\circ ~\] done clear
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• question_answer25)
  ACBD is a quadrilateral in which AC = AD and AB is the angle bisector of\[\angle CAD.\]By which congruence rule is congruence\[\Delta ACB\cong \Delta ADB?\]
  A)
   S.S.S.                         done clear
  B)
   R.H.S.            done clear
  C)
        S.A.S.             done clear
  D)
        A.S.A. done clear
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• question_answer26)
  In the adjacent figure, C is the mid point of AB, \[\angle CAD=\angle CBE\]and \[\angle ACE=\angle BCD.\] By which congruency condition\[\Delta DAC\cong \Delta EBC?\]
  A)
   R.H.S.            done clear
  B)
        S.S.S.             done clear
  C)
        S.A.S.             done clear
  D)
        A.S.A. done clear
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• question_answer27)
  If \[\Delta XYZ\]and \[\Delta STU\]are to be congruent by A.S.A identify the additional information needed.
  A)
  \[\angle S=\angle Y\]           done clear
  B)
                              \[\overline{XZ}=\overline{SU}\]        done clear
  C)
                   \[\angle XYZ=\angle STU\]   done clear
  D)
                   \[\overline{YZ}=\overline{TU}\]                    done clear
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• question_answer28)
  Which triangle is not congruent to the other three
  A)
    done clear
  B)
                     done clear
  C)
  done clear
  D)
       done clear
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• question_answer29)
  If \[\Delta ABC\cong \Delta PQR\]and \[\Delta ABC\]is not congruent to \[\Delta RPQ,\]which of the following is not true?
  A)
   \[BC=PQ\]                 done clear
  B)
  \[AC=PR\]      done clear
  C)
       \[AB=PQ\]      done clear
  D)
       \[QR=BC\] done clear
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• question_answer30)
  If\[\Delta ABC\cong \Delta PRQ,\]identify the corresponding angle and side equal to \[\angle B\]and side \[PQ.\]
  A)
  \[\angle P\]and AC                   done clear
  B)
  \[\angle R\]and BC       done clear
  C)
  \[\angle R\]and AC       done clear
  D)
       \[\angle Q\]and AB done clear
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• question_answer31)
  Consider the following statements. (i)  If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent. (ii) If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent. Of these two statements, which of the following is correct?
  A)
   (i) is true and (ii) is false. done clear
  B)
   Both (i) and (ii) are false. done clear
  C)
   Both (i) and (ii) are true. done clear
  D)
   (i) is false and (ii) is true. done clear
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• question_answer32)
  Identify the property by which \[\Delta ADB\cong \Delta ADC\]in the following figure.
  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_answer33)
  In the given figure, AB = CD and AD = BC. Which of the following congruency rules is suitable to prove that \[\Delta BCA\cong \Delta DAC?\]
  A)
   S.S.S.                         done clear
  B)
   R.H.S.            done clear
  C)
        S.A.S.             done clear
  D)
        A.S.A. done clear
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• question_answer34)
  In the given figure, it is given that ML = MN, QM = MR, \[ML\bot PQ\]and\[MN\bot PR.\] Which of the following congruency rules is suitable to prove that\[PQ=PR?\]
  A)
   S.A.S.             done clear
  B)
        A.A.A.             done clear
  C)
   R.A.S.             done clear
  D)
        S.S.S. done clear
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• question_answer35)
  How many congruent trapeziums are there in the given figure?
  A)
   8                     done clear
  B)
        16                   done clear
  C)
        12                   done clear
  D)
        21 done clear
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• question_answer36)
  A: If the hypotenuse and an acute angle of one right triangle is equal to the hypotenuse and corresponding acute angle of another right triangle, those two triangles are congruent. R: Two right angles are congruent by R.H.S. property. Which of the following statements is true?
  A)
   A is true and R is the correct explanation of A. done clear
  B)
   A is false and R is not the correct explanation of A. done clear
  C)
   A is false and R is false. done clear
  D)
   A is false and R is true. done clear
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• question_answer37)
  By which congruence condition are the two triangles in the given figure congruent?
  A)
   S.A.S.                         done clear
  B)
   R.H.S.            done clear
  C)
   S.S.S.             done clear
  D)
        A.S.A. done clear
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• question_answer38)
  Which triangle is not congruent to the other three?
  A)
             done clear
  B)
  done clear
  C)
        done clear
  D)
       done clear
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• question_answer39)
  How many triangles are congruent to A ABE in the given figure?
  A)
   8                                 done clear
  B)
   9                     done clear
  C)
   7                     done clear
  D)
        16 done clear
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