9th Class Mathematics Triangles Question Bank

done Triangles Total Questions - 50

• question_answer1)
  Given \['p'\] is the exterior angle of \[\Delta PQR\] and \['q+r'\] is the sum of interior angles opposite to\['p'\]. Which of the following is true?
  A)
  \[p+r=q\]                      done clear
  B)
  \[p=q+r\]          done clear
  C)
  \[p+q=r\]          done clear
  D)
         \[r=q-p\] done clear
  View Solution play_arrow

• question_answer2)
  Identify the interior opposite angles of the exterior angle \[\angle ACD\] of\[\Delta ABC\].
  A)
   \[\angle B,\,\angle C\] done clear
  B)
   \[\angle A,\,\angle C\] done clear
  C)
   \[\angle A,\,\angle B\] done clear
  D)
   \[\angle B,\,\angle D\] done clear
  View Solution play_arrow

• question_answer3)
  A student is asked to draw a triangle whose angles are \[{{90}^{o}},\,\,{{90}^{o}}\] and\[{{20}^{o}}\]. Which of the following is possible with the given measures?
  A)
   He can draw a right angled triangle. done clear
  B)
   He can draw an equilateral triangle. done clear
  C)
   He cannot draw any triangle. done clear
  D)
   He can draw an obtuse angled triangle. done clear
  View Solution play_arrow

• question_answer4)
  In the given figure, find the ratio\[\angle ABC:\angle ACD\].
  A)
  \[1:1\]                            done clear
  B)
  \[2:1\]                done clear
  C)
  \[1:2\]                done clear
  D)
         \[3:1\]                done clear
  View Solution play_arrow

• question_answer5)
  In\[\Delta ABC\], \[AD\bot BC\]and\[\angle B=\angle C\]. By which property is\[\Delta ADB\cong \Delta ADC\]?
  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
  View Solution play_arrow

• question_answer6)
  An exterior angle of a triangle is \[{{180}^{o}}\] and one of the interior opposite angles is\[{{30}^{o}}\]. Find the other two angles of the triangle.
  A)
  \[{{80}^{o}},\,\,{{70}^{o}}\]             done clear
  B)
  \[{{70}^{o}},\,\,{{40}^{o}}\] done clear
  C)
         \[{{110}^{o}},\,\,{{40}^{o}}\]           done clear
  D)
         \[{{110}^{o}},\,\,{{75}^{o}}\]           done clear
  View Solution play_arrow

• question_answer7)
  One of the angles of a triangle is\[{{75}^{o}}\]. If the difference of the other two angles is\[{{35}^{o}}\], what is the measure the largest angle of the triangle?
  A)
  \[{{80}^{o}}\]                         done clear
  B)
  \[{{75}^{o}}\]             done clear
  C)
         \[{{100}^{o}}\]                       done clear
  D)
         \[{{100}^{o}}\] done clear
  View Solution play_arrow

• question_answer8)
  In the figure, if \[AB=CF,\,\,EF=BD\] and\[\angle AFE=\angle DBC\], by which condition is \[\Delta AFE\]to\[\Delta CBD\]?
  A)
   S.A.S.                          done clear
  B)
   S.S.S.  done clear
  C)
          A.S.A.              done clear
  D)
          R.H.S. done clear
  View Solution play_arrow

• question_answer9)
  In the given figure\[\Delta ABD\cong \Delta ACD\]\[AB=AC\],\[BC=CD\] By which criterion are the triangles 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
  View Solution play_arrow

• question_answer10)
  In the given figure, \[AD\] is the bisector of \[\angle A\] and\[AB=AC\]. By which criterion are \[\Delta ABD\] and \[\Delta ACD\]congruent? (i)  S.S.S.                      (ii) S.A.S.                      (iii) A.SA                       (iv) R.H.S.                    
  A)
   (i) only             done clear
  B)
          (ii), (iii) and (iv) only                   done clear
  C)
          (i) and (iii)                     done clear
  D)
          (ii) and (iv) only done clear
  View Solution play_arrow

• question_answer11)
  In quadrilateral\[ACBD\], \[AB\] is a diagonal. If \[AC=AD\] and \[AB\] bisects\[\angle A\], by which congruence property is?
  A)
   S.A.S.    done clear
  B)
                      A.S.A.  done clear
  C)
          S.S.S.              done clear
  D)
          R.H.S.              done clear
  View Solution play_arrow

• question_answer12)
  In the given figure, \[\angle Q<\angle P\] and\[\angle R<\angle S\]. Which of the following is true?
  A)
  \[PS<QR\]                     done clear
  B)
         \[PS>QR\]         done clear
  C)
         \[QR=PS\]         done clear
  D)
          Either (b) or (c). done clear
  View Solution play_arrow

• question_answer13)
  In the given figure, if \[AB=AC\] and\[BD=DC\], by which criterion are \[\Delta ABD\] and \[\Delta ACD\] congruent?
  A)
   S.S.S.              done clear
  B)
          A.S.A.  done clear
  C)
          S.A.S.              done clear
  D)
          R.H.S.              done clear
  View Solution play_arrow

• question_answer14)
  In\[\Delta ABC\],\[AB=AC\]and\[AD\]is perpendicular to\[BC\]. State the property by which\[\Delta ADB\cong \Delta ADC\]
  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
  View Solution play_arrow

• question_answer15)
  \[\Delta ABC\]is an isosceles triangle with   \[AB=AC\]. If\[AD\bot BC\], which of the following is true?
  A)
  \[\angle B>\angle C\]                  done clear
  B)
         \[\angle B=\angle C\]      done clear
  C)
         \[\angle B<\angle C\]                  done clear
  D)
         \[\angle A=\angle B=\angle C\]                done clear
  View Solution play_arrow

• question_answer16)
  By which congruence property, are the two triangles in the figure congruent?
  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
  View Solution play_arrow

• question_answer17)
  In the given figure, if \[AD=BC\] and \[AD||BC\] which of the following holds good?
  A)
  \[AB=AD\]                    done clear
  B)
         \[AB=DC\]        done clear
  C)
         \[BC=CD\]                    done clear
  D)
         \[AB=AC\] done clear
  View Solution play_arrow

• question_answer18)
  In the given figure, if \[AB=AC\] and\[BD=DC\], find the measure of\[\angle ADC\].
  A)
  \[{{60}^{o}}\]                         done clear
  B)
         \[{{120}^{o}}\]                       done clear
  C)
         \[{{90}^{o}}\]                         done clear
  D)
         \[{{110}^{o}}\]           done clear
  View Solution play_arrow

• question_answer19)
  If\[\Delta ABC\cong \Delta PQR\], which of the following is true?
  A)
  \[AB=RP\]         done clear
  B)
         \[CA=RP\]         done clear
  C)
         \[AC=RQ\]                    done clear
  D)
         \[CB=QP\] done clear
  View Solution play_arrow

• question_answer20)
  Which of the following is incorrect?
  A)
   If two triangles have their corresponding sides equal, then they are congruent done clear
  B)
          If two triangles have their corresponding angles equal, then they are congruent. done clear
  C)
          If two circles have the same radii then they are congruent. done clear
  D)
          If two squares have the same length of their sides, then they are congruent. done clear
  View Solution play_arrow

• question_answer21)
  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 triangle are equal to the corresponding two sides and the included angle of the other. 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 false. done clear
  View Solution play_arrow

• question_answer22)
  Which of the following statements is true?
  A)
   Two line segments having the same length are congruent. done clear
  B)
          Two squares having the same side length are congruent. done clear
  C)
          Two circles having the same radius are congruent. done clear
  D)
          All the above. done clear
  View Solution play_arrow

• question_answer23)
  Which of the following is true about the difference of any two sides of a triangle?
  A)
   It is greater than the third side. done clear
  B)
          It is zero. done clear
  C)
          It is lesser than the third side done clear
  D)
          It is lesser than zero. done clear
  View Solution play_arrow

• question_answer24)
  In the figure given, find\[\angle x\].
  A)
  \[{{40}^{o}}\]                         done clear
  B)
         \[{{110}^{o}}\]                       done clear
  C)
         \[{{45}^{o}}\]                         done clear
  D)
         \[{{65}^{o}}\]             done clear
  View Solution play_arrow

• question_answer25)
  In\[\Delta LMN\], if\[\angle M={{90}^{o}}\], which of the following is true?
  A)
   \[NL\]is the longest side. done clear
  B)
          \[LM\]is the longest side. done clear
  C)
          \[MN\]is the longest side. done clear
  D)
          \[NL\]is the shortest side. done clear
  View Solution play_arrow

• question_answer26)
  Which of the following statement(s) is/are false?
  A)
   Two triangles having the same area are congruent. done clear
  B)
          If two sides and one angle of a triangle are equal to the corresponding two sides and the angle of another triangle, then the two triangles are congruent. done clear
  C)
          If the hypotenuse of one right triangle is equal to the hypotenuse of another triangle, then the triangles are congruent. done clear
  D)
          All the above. done clear
  View Solution play_arrow

• question_answer27)
  It is not possible to construct a triangle with which of the following sides?
  A)
   \[8.3\,\,cm,\,\,3.4\,\,cm,\,\,6.1\,\,cm\] done clear
  B)
          \[5.4\,\,cm,\,\,2.3\,\,cm,\,\,3.1\,\,cm\] done clear
  C)
          \[6\,\,cm,\,\,7\,\,cm,\,\,10\,\,cm\] done clear
  D)
          \[3\,\,cm,\,\,5\,\,cm,\,\,5\,\,cm\] done clear
  View Solution play_arrow

• question_answer28)
  In\[\Delta ABC\], if\[AB=BC\], which of the following statements is necessarily true?
  A)
  \[\angle B=\angle C\]                  done clear
  B)
         \[\angle A=\angle C\]      done clear
  C)
         \[\angle A=\angle B\]                  done clear
  D)
         \[\angle A<\angle C\]   done clear
  View Solution play_arrow

• question_answer29)
  If\[\Delta ABC\cong \Delta DEF\]by S.A.S. congruence rule, which of the following could be the equivalent measures?
  A)
  \[AB=DE,\,\,BC=EF,\,\,\angle B=\angle E\] done clear
  B)
         \[AB=DE,\,\,BC=EF,\,\,\angle D=\angle A\] done clear
  C)
         \[AB=DE,\,\,BC=EF,\,\,\angle C=\angle F\] done clear
  D)
         \[AB=DE,\,\,BC=EF,\,\,CA=FD\] done clear
  View Solution play_arrow

• question_answer30)
  In \[\Delta ABC,\] \[AB=5\,\,cm,\] \[BC=6\,\,cm\] and\[CA=7\,\,cm\]. Identify the relation between the angles.
  A)
  \[ZB>ZA>ZC\]   done clear
  B)
         \[ZA>ZB>ZC\]   done clear
  C)
         \[ZB>ZC>ZA\]   done clear
  D)
         \[ZB>ZA>ZC\]   done clear
  View Solution play_arrow

• question_answer31)
  In triangles \[ABC\] and\[DEF\], \[AB=FD\] and\[\angle A=\angle D\]. Which of the following is true if the two triangles are congruent by S.A.S. axiom?
  A)
  \[BC=EF\]         done clear
  B)
         \[AC=DE\]         done clear
  C)
         \[AC=EF\]                     done clear
  D)
         \[BC=DE\]                     done clear
  View Solution play_arrow

• question_answer32)
  If \[\Delta ABC\cong \Delta DEF\] by S.S.S. congruence rule, which of the following options holds true?
  A)
  \[\angle A>\angle D\] done clear
  B)
         \[\angle A=\angle D,\,\,\angle B=\angle E,\,\,\angle C=\angle F\] done clear
  C)
         \[\angle B<\angle E\] done clear
  D)
         \[\angle C=\angle F\] done clear
  View Solution play_arrow

• question_answer33)
  In the given figure, \[ABCD\] is a quadrilateral in which\[AB=BC\]and\[AD=DC\]. Find the measure of\[\angle BCD\].
  A)
  \[{{150}^{o}}\]                                   done clear
  B)
         \[{{30}^{o}}\] done clear
  C)
         \[{{105}^{o}}\]                                   done clear
  D)
         \[{{72}^{o}}\] done clear
  View Solution play_arrow

• question_answer34)
  If \[\Delta ABC\cong \Delta DEF\] by S.S.S. congruence rule, which of the following statements is true?
  A)
  \[AB=EF,\,\,BC=FD,\,\,CA=DE\] done clear
  B)
         \[AB=FD,\,\,BC=DE,\,\,CA=EF\] done clear
  C)
         \[AB=DE,\,\,BC=EF,\,\,CA=FD\] done clear
  D)
         \[AB=DE,\,\,BC=EF,\,\,\angle C=\angle F\] done clear
  View Solution play_arrow

• question_answer35)
  In\[\Delta ABC\], if \[\angle A={{50}^{o}}\] and\[\angle B={{60}^{o}}\], what is the greatest side?
  A)
   \[AB\]                           done clear
  B)
          \[BC\]               done clear
  C)
          \[AC\]                           done clear
  D)
          can?t be determined done clear
  View Solution play_arrow

• question_answer36)
  In\[\Delta ABD\], if\[\angle B=\angle C\], which of the following is true?
  A)
  \[BC=AB\]                    done clear
  B)
         \[AC=BC\]        done clear
  C)
         \[AB=AC\]                    done clear
  D)
         \[AB>AC\]                    done clear
  View Solution play_arrow

• question_answer37)
  In\[\Delta ABC,\]\[\angle ={{50}^{o}},\,\,\angle B={{60}^{o}}\]. What is the ascending order of the sides of the triangle?
  A)
  \[AB<BC<CA\] done clear
  B)
         \[CA<AB<BC\] done clear
  C)
         \[BC<CA<AB\] done clear
  D)
         \[BC<AB<CA\] done clear
  View Solution play_arrow

• question_answer38)
  In\[\Delta DEF\], which of the following statements is true?
  A)
  \[DE+EF=FD\]   done clear
  B)
         \[DE+EF<FD\]   done clear
  C)
         \[DE>EF+FD\]   done clear
  D)
         \[DE+EF>FD\] done clear
  View Solution play_arrow

• question_answer39)
  \[\Delta ABC\cong \Delta PQR\], if \[AB=5\,\,cm,\] \[\angle B={{40}^{o}}\]and\[\angle A={{80}^{o}}\], which of the following is true?
  A)
  \[QP=5\,\,cm,\,\,\angle P={{60}^{o}}\] done clear
  B)
         \[QP=5\,\,cm,\,\,\angle R={{60}^{o}}\] done clear
  C)
         \[QP=5\,\,cm,\,\,\angle R={{60}^{o}}\] done clear
  D)
         \[QP=5\,\,cm,\,\,\angle Q={{40}^{o}}\] done clear
  View Solution play_arrow

• question_answer40)
  In\[\Delta ABC\], if \[AD\] is the perpendicular bisector of\[BC\], which of the following is true?
  A)
  \[AB>AC\]                    done clear
  B)
         \[AD=AB\]        done clear
  C)
         \[AB=AC\]                    done clear
  D)
         \[AD=AC\]                    done clear
  View Solution play_arrow

• question_answer41)
  In\[\Delta ABC\], if \[AD\] is a median, what is the relation between the sides?
  A)
  \[AB+AC>AD\] done clear
  B)
         \[AB+AC<2AD\] done clear
  C)
         \[AB+AC=2AD\]           done clear
  D)
         \[AB+AC>2AD\]           done clear
  View Solution play_arrow

• question_answer42)
  Which of the following statements is correct?
  A)
   A triangle can have two right angles. done clear
  B)
          A triangle can have two obtuse angles. done clear
  C)
          A triangle can have all angles more than\[{{60}^{o}}\]. done clear
  D)
          A triangle can have two acute angles. done clear
  View Solution play_arrow

• question_answer43)
  An exterior angle of a triangle is \[{{120}^{o}}\] and the two interior opposite angles are equal. Find the value of each interior angle.
  A)
  \[{{60}^{o}}\]                         done clear
  B)
         \[{{100}^{o}}\]                       done clear
  C)
         \[{{120}^{o}}\]                                   done clear
  D)
         \[{{180}^{o}}\] done clear
  View Solution play_arrow

• question_answer44)
  In a right triangle, the two acute angles are in the ratio\[4:5\]. Find them respectively.
  A)
  \[{{50}^{o}},\,\,{{40}^{o}}\]             done clear
  B)
         \[{{40}^{o}},\,\,{{50}^{o}}\] done clear
  C)
         \[{{45}^{o}},\,\,{{55}^{o}}\]             done clear
  D)
         \[{{30}^{o}},\,\,{{60}^{o}}\] done clear
  View Solution play_arrow

• question_answer45)
  In\[\Delta ABC\], if\[AB>BC\], which of the following is true?
  A)
  \[\angle C<\angle A\]                  done clear
  B)
         \[\angle C=\angle A\]      done clear
  C)
         \[\angle C>\angle A\]                  done clear
  D)
         \[\angle A=\angle B\] done clear
  View Solution play_arrow

• question_answer46)
  In the figure given,\[~AB=AC,\] \[E\] is midpoint of \[AB\] and \[F\] is midpoint of\[AC\]. What is the length of\[BF\]?    
  A)
  \[AE\]                            done clear
  B)
         \[CF\]                done clear
  C)
         \[BE\]                            done clear
  D)
         \[CE\] done clear
  View Solution play_arrow

• question_answer47)
  In the figure given, if\[DA=DB=DC\], find\[\angle ACB\]
  A)
  \[{{70}^{o}}\]                         done clear
  B)
         \[{{90}^{o}}\]             done clear
  C)
         \[{{100}^{o}}\]                                   done clear
  D)
         \[{{120}^{o}}\]                       done clear
  View Solution play_arrow

• question_answer48)
  \[\Delta ABC\] is right angled at\[A\]. \[AB=60\] units, \[AC=60\] units, and\[BC=100\]units. \[D\] is a point between \[B\] and \[C\] such that triangles \[ADB\] and \[ADC\] have equal perimeters. What is the length of\[BD\]?
  A)
   \[10\] units                    done clear
  B)
          \[20\] units                    done clear
  C)
          \[40\] unis                     done clear
  D)
          \[60\] units        done clear
  View Solution play_arrow

• question_answer49)
  If the length of the largest side of a triangle is\[12\,\,cm\], find the possible values of its other two sides.
  A)
  \[4.8,\,\,8.2\]                  done clear
  B)
         \[3.2,\,\,6.5\]      done clear
  C)
         \[2.9,\,\,7.2\]                  done clear
  D)
         \[4.1,\,\,3.9\]                  done clear
  View Solution play_arrow

• question_answer50)
  In the figure given, \[DP=BQ,\] and\[\angle ADP=\angle CBQ\]. To which triangle is\[\angle ADP\] congruent to?
  A)
  \[\Delta CBQ\]                done clear
  B)
         \[\Delta PDQ\]                done clear
  C)
         \[\Delta QBC\]                done clear
  D)
         \[\Delta PQB\] done clear
  View Solution play_arrow