7th Class Mathematics The Triangle and its Properties Question Bank

done Triangles Total Questions - 51

• question_answer1)
  A In a \[\Delta ABC,\] if \[A{{B}^{2}}=B{{C}^{2}}+A{{C}^{2}},\]at which vertex is the right angle?
  A)
   A            done clear
  B)
   B done clear
  C)
   C              done clear
  D)
   Either A or B done clear
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• question_answer2)
  Which type of triangle is formed by \[BC=7.2\,\,cm,\] \[AC=6\text{ }cm\] and \[\angle {{120}^{o}}\]?
  A)
   An acute angled triangle. done clear
  B)
   An obtuse angled triangle.   done clear
  C)
   A right angled triangle. done clear
  D)
   An isosceles triangle. done clear
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• question_answer3)
  Which triangle is formed by \[AB=3\text{ }cm,\] \[BC=4\text{ }cm\] and \[AC=8\text{ }cm\]?
  A)
   A scalene triangle. done clear
  B)
   An isosceles triangle. done clear
  C)
   An equilateral triangle. done clear
  D)
   No triangle is formed.   done clear
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• question_answer4)
  A If two angles in a triangle are \[{{65}^{o}}\] and \[{{85}^{o}},\] what is the third angle?
  A)
   \[{{30}^{o}}\]     done clear
  B)
          \[{{45}^{o}}\]   done clear
  C)
   \[{{60}^{o}}\]    done clear
  D)
          \[{{90}^{o}}\] done clear
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• question_answer5)
  If one angle is the average of the other two angles and the difference between the greatest and least angles is \[{{60}^{o}},\] which triangle is formed?                    
  A)
   An isosceles triangle. done clear
  B)
   An equilateral triangle. done clear
  C)
   A right angled triangle.   done clear
  D)
   A right angled isosceles triangle. done clear
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• question_answer6)
  In \[\Delta ABC,\] if \[AB=BC\] and \[\angle B={{80}^{o}}\] what is the measure of \[\angle C\]?
  A)
   \[{{50}^{o}}\]                                      done clear
  B)
   \[{{100}^{o}}\] done clear
  C)
   \[{{130}^{o}}\]                 done clear
  D)
          \[{{180}^{o}}\] done clear
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• question_answer7)
  7.            Which triangle is formed  by \[BC=AC=7.2\,cm\]    and \[\angle C={{90}^{o}}\]?
  A)
   A right angled triangle. done clear
  B)
   An isosceles triangle. done clear
  C)
   A right angled isosceles triangle.   done clear
  D)
   No triangle is formed. done clear
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• question_answer8)
  Which of the following statements is false?
  A)
   The sum of two sides of a triangle is greater than the third side. done clear
  B)
   In a right angled triangle, hypotenuse is the longest side. done clear
  C)
   A, B and C are collinear if \[AB+BC=AC\]. done clear
  D)
   The sum of angles in a triangle is less than \[{{180}^{o}}\].   done clear
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• question_answer9)
  What is the length of the hypotenuse of a right angled triangle whose two legs measure \[12\text{ }cm\] and\[0.35\text{ }m\]?
  A)
   \[37cm\]               done clear
  B)
          \[3.72\,cm\] done clear
  C)
   \[0.372\,cm\]                    done clear
  D)
          \[37\,m\] done clear
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• question_answer10)
  If the two legs of a right angled triangle are equal and the square of the hypotenuse is \[100\text{ }sq\] units, what is the length of each leg?
  A)
   10 units done clear
  B)
        \[5\sqrt{2}\] units   done clear
  C)
   \[10\sqrt{2}\] units done clear
  D)
   15 units done clear
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• question_answer11)
  In a \[\Delta PQR,\,\,PQ=PR\] and \[\angle Q\] is twice that of \[\angle P\]. What is the measure of \[\angle Q\]?
  A)
   \[{{72}^{o}}\]      done clear
  B)
          \[{{36}^{o}}\] done clear
  C)
   \[{{144}^{o}}\] done clear
  D)
          \[{{108}^{o}}\] done clear
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• question_answer12)
  If two sides of an isosceles triangle are \[3\,\,cm\] and \[8\,\,cm,\] what is the length of the third side?
  A)
   \[3\,\,cm\]        done clear
  B)
   \[8\,\,cm,\]   done clear
  C)
   \[3\,\,cm\] or \[8\,\,cm,\] done clear
  D)
   Neither [a] nor [b] done clear
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• question_answer13)
  If in a \[\Delta ABC,\,\,\angle A={{60}^{o}}\] and \[AB=AC,\]of what type is \[\Delta \,ABC\]?
  A)
   An isosceles triangle. done clear
  B)
   A right angled triangle. done clear
  C)
   An isosceles right angled triangle. done clear
  D)
   An equilateral triangle.   done clear
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• question_answer14)
  In a \[\Delta \,ABC,\]if \[AB+BC=10cm,\] \[BC+CA=12cm\], \[CA+AB=16\text{ }cm,\]what is the sum of the lengths of its sides?
  A)
   \[19\,cm\]            done clear
  B)
          \[17\,cm\] done clear
  C)
   \[38\,cm\]          done clear
  D)
          \[30\,cm\] done clear
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• question_answer15)
  Which of the following are the angles in a right angled triangle other than the right angle?
  A)
   Acute angles   done clear
  B)
   Obtuse angles done clear
  C)
   Right angles done clear
  D)
   Reflex angles done clear
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• question_answer16)
  In a \[\Delta \,ABC,\] if \[\angle A=\angle B+\angle C,\]what is the measure of \[\angle A\]
  A)
   \[{{60}^{o}}\]    done clear
  B)
          \[{{45}^{o}}\] done clear
  C)
   \[{{90}^{o}}\]                      done clear
  D)
          \[{{135}^{o}}\] done clear
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• question_answer17)
  If a, b and c are the sides of a triangle, which of the following is correct?
  A)
   \[a-b>c\]            done clear
  B)
          \[c>a+b\] done clear
  C)
   \[c=a+b\]           done clear
  D)
          \[b<c+a\]   done clear
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• question_answer18)
  If the angles of a triangle are in the ratio \[1:2:7,\]what type of a triangle is it?
  A)
   An acute angled triangle. done clear
  B)
   An obtuse angled triangle.   done clear
  C)
   A right angled triangle. done clear
  D)
   A right angled isosceles triangle. done clear
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• question_answer19)
  A triangle always has
  A)
   exactly one acute angle, done clear
  B)
   exactly two acute angles. done clear
  C)
   at least two acute angles.   done clear
  D)
   exactly 2 right angles. done clear
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• question_answer20)
  How many independent measurements are required to construct a triangle?
  A)
   \[3\]                       done clear
  B)
          \[4\] done clear
  C)
   \[2\]                     done clear
  D)
           \[5\] done clear
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• question_answer21)
  In a \[\Delta ABC,\] if \[\angle B\] is an obtuse angle, which is the longest side?
  A)
   AB          done clear
  B)
   BC done clear
  C)
   AC            done clear
  D)
   Either [a] or [b] done clear
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• question_answer22)
  If P: An isosceles triangle is right angled. \[Q:\angle A=\angle B={{45}^{o}}\] and \[\angle C={{90}^{o}}\] which  of the following statements is true?
  A)
   P is true and Q is the correct explanation of P.   done clear
  B)
   P is true and Q is not the correct explanation of P. done clear
  C)
   P is false. done clear
  D)
   P is the correct explanation of Q. done clear
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• question_answer23)
  An isosceles triangle can be obtuse angled.
  A)
   Always false. done clear
  B)
   Always true. done clear
  C)
   Cannot be determined. done clear
  D)
   Sometimes false.   done clear
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• question_answer24)
  Which of the following statements is correct?
  A)
   The difference of any two sides is less than the third side. done clear
  B)
   A triangle cannot have two obtuse angles. done clear
  C)
   A triangle cannot have an obtuse angle and a right angle. done clear
  D)
   All the above.   done clear
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• question_answer25)
  Two chimneys 18m and 13m high stand upright on a ground. If their feet are 12m apart, what is the distance between their tops?
  A)
   \[5\,m\]                              done clear
  B)
          \[31\,m\] done clear
  C)
   \[13\,m\]              done clear
  D)
          \[18\,m\] done clear
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• question_answer26)
  The top of a broken tree touches the ground at a distance of 15 m from its base. If the tree is broken at a height of 8 m from the ground, what is the actual height of the tree?
  A)
   \[20\,m\]            done clear
  B)
          \[25\,m\]   done clear
  C)
   \[30\,m\]            done clear
  D)
          \[17\,m\] done clear
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• question_answer27)
  What is the ratio in which the centroid of a triangle divides the medians?
  A)
   \[1:2\] done clear
  B)
          \[1:3\] done clear
  C)
   \[2:1\]   done clear
  D)
          \[3:1\] done clear
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• question_answer28)
  The centroid of a triangle is the point of concurrence of which of these?
  A)
   Angle bisectors done clear
  B)
   Perpendicular bisectors done clear
  C)
   Altitudes done clear
  D)
   Medians   done clear
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• question_answer29)
  Which of the following statements is true?
  A)
   The centroid of an acute angled triangle lies in the interior of the triangle. done clear
  B)
   The ortho centre of an acute angled triangle lies in the interior of the triangle. done clear
  C)
   The medians of a triangle are concurrent. done clear
  D)
   All the above.   done clear
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• question_answer30)
  In  \[\Delta ABC,\,\,D\] is the midpoint of BC and G is ^^ the centroid of the triangle. If \[GD=2\text{ }cm,\]what is the length of AD?
  A)
   \[4\,\,cm\]                         done clear
  B)
   \[6\,\,cm\]   done clear
  C)
   \[2\,\,cm\]         done clear
  D)
          \[8\,\,cm\] done clear
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• question_answer31)
  In a \[\Delta ABC,\,E\] is the midpoint of AC and G is the centroid of the triangle. What is \[BE:GE\]?
  A)
   \[1:2\]                                  done clear
  B)
   \[2:1\] done clear
  C)
   \[3:1\]    done clear
  D)
  \[1:3\] done clear
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• question_answer32)
  Which of the following statements is true?
  A)
   The ortho centre of a right angled triangle is the vertex containing the right angle. done clear
  B)
   The median of a triangle joins a vertex to the midpoint of the opposite side. done clear
  C)
   The centroid of a right angled triangle lies in the interior of the triangle. done clear
  D)
   All the above.   done clear
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• question_answer33)
  In a scalene triangle ABC, X is the midpoint of BC. What is AX?
  A)
   Median                 done clear
  B)
          Altitude done clear
  C)
   Centroid             done clear
  D)
          Ortho centre done clear
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• question_answer34)
  In \[\Delta PQR,\] \[PQ=PR;\]M is a point on QR and \[PM\bot OR\] .What do you call PM?
  A)
   Centroid             done clear
  B)
          Median done clear
  C)
   Altitude                 done clear
  D)
          Vertex done clear
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• question_answer35)
  In \[\Delta XYZ,\] XP is the median. Which of the following is correct?
  A)
   \[XP=XY\]           done clear
  B)
          \[YP=PZ\]   done clear
  C)
   \[XP=XZ\]           done clear
  D)
          \[XY=XZ\] done clear
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• question_answer36)
  From the figure given, which of the following statements is true?
  A)
                   \[\angle x+\angle y=\angle 1+\angle 3\] done clear
  B)
                   \[\angle y=\angle 2\] done clear
  C)
                   \[\angle x=\angle 1\] done clear
  D)
                   \[\angle x+\angle y=\angle 1+\angle 2\]   done clear
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• question_answer37)
  The exterior angle of a triangle is \[{{110}^{o}}\]. If one of the interior opposite angles is \[{{55}^{o}},\]what is the measure of the other?
  A)
   \[{{45}^{o}}\]                    done clear
  B)
   \[{{65}^{o}}\]   done clear
  C)
   \[{{55}^{o}}\]     done clear
  D)
          \[{{35}^{o}}\] done clear
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• question_answer38)
  In \[\Delta PQR,\,\,\angle Q={{90}^{o}}\]. Which of the following is the longest side?
  A)
   RQ          done clear
  B)
   PQ done clear
  C)
   PR             done clear
  D)
   Either [a] or [b] done clear
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• question_answer39)
  Which of the following statements is NOT true?
  A)
   A triangle can have three 60° angles. done clear
  B)
   A triangle can have a right angle. done clear
  C)
   A triangle can have two right angles.   done clear
  D)
   A triangle can have all three angles equal. done clear
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• question_answer40)
  From the following figure, what are the respective values of x and y?
  A)
   \[{{80}^{o}},{{60}^{o}}\]         done clear
  B)
   \[{{60}^{o}},{{40}^{o}}\] done clear
  C)
   \[{{60}^{o}},{{80}^{o}}\]     done clear
  D)
   \[{{40}^{o}},{{60}^{o}}\] done clear
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• question_answer41)
  Angles of a triangle are \[(x+{{10}^{o}}),\,\,(x+{{40}^{o}})\]and \[(2x-{{30}^{o}})\]. What is the value of x?
  A)
   \[{{30}^{o}}\]   done clear
  B)
          \[{{40}^{o}}\]    done clear
  C)
   \[{{20}^{o}}\]    done clear
  D)
          \[{{10}^{o}}\] done clear
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• question_answer42)
  In the figure given, what are the values of \[\angle b,\,\,\angle c\] and \[\angle a\] respectively?                                
  A)
                   \[{{18}^{o}},{{70}^{o}}\] and \[{{92}^{o}}\] done clear
  B)
                   \[{{92}^{o}},\,{{70}^{o}}\] and \[{{18}^{o}}\] done clear
  C)
                   \[{{70}^{o}},{{92}^{o}}\] and \[{{18}^{o}}\]   done clear
  D)
                   \[{{70}^{o}},{{18}^{o}}\] and \[{{92}^{o}}\] done clear
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• question_answer43)
  In  \[\Delta ABC,\]  \[AB=AC,\]  \[\angle A={{40}^{o}}\] ,O is a point inside \[\Delta ABC\] such that \[\angle OBC=\angle OCA\]. Find the measure of \[\angle BOC\].
  A)
                   \[{{110}^{o}}\]   done clear
  B)
                          \[{{35}^{o}}\] done clear
  C)
                   \[{{140}^{o}}\] done clear
  D)
          \[{{155}^{o}}\] done clear
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• question_answer44)
  The triangle XYZ is right angled at X .Which is the longest side of \[\Delta XYZ\]?
  A)
   XY          done clear
  B)
                          XZ   done clear
  C)
   ZX                          done clear
  D)
          YZ   done clear
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• question_answer45)
  Which of the following statements is correct?
  A)
   The exterior angle of a triangle is equal to its interior adjacent angle. done clear
  B)
   The median of a triangle joins its vertex to the midpoint of its opposite side.   done clear
  C)
   The altitude of a triangle is drawn from a vertex to the midpoint of the opposite side. done clear
  D)
   All the above. done clear
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• question_answer46)
  What is the number of medians in a triangle?
  A)
   0                             done clear
  B)
          2    done clear
  C)
   3                                               done clear
  D)
   1 done clear
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• question_answer47)
  Find the measure of y in the given figure.
  A)
   \[{{30}^{o}}\]     done clear
  B)
          \[{{60}^{o}}\]   done clear
  C)
   \[{{90}^{o}}\]   done clear
  D)
          \[{{120}^{o}}\] done clear
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• question_answer48)
  A In the figure, \[AB=AC\] and \[AD||BC\] Find the respective measures of x, y and z.
  A)
                   \[x={{70}^{o}},y={{70}^{o}},z={{55}^{o}}\] done clear
  B)
                   \[x={{70}^{o}},y={{55}^{o}},z={{55}^{o}}\]   done clear
  C)
                   \[x={{55}^{o}},y={{55}^{o}},z={{55}^{o}}\] done clear
  D)
                   \[x={{70}^{o}},y={{55}^{o}},z={{70}^{o}}\] done clear
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• question_answer49)
  Find the angles x and y respectively.
  A)
                   \[x={{47}^{o}},y={{25}^{o}}\] done clear
  B)
                   \[x={{27}^{o}},y={{45}^{o}}\] done clear
  C)
                   \[x={{45}^{o}},y={{27}^{o}}\]   done clear
  D)
                   \[x={{25}^{o}},y={{47}^{o}}\] done clear
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• question_answer50)
  Find the value of x.
  A)
                   \[{{106}^{o}}\] done clear
  B)
                          \[{{53}^{o}}\] done clear
  C)
                   \[{{26}^{o}}\]                      done clear
  D)
          \[{{52}^{o}}\] done clear
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• question_answer51)
  Find the measure of x in the following figure.
  A)
                   \[{{112}^{o}}\]   done clear
  B)
                          \[{{56}^{o}}\] done clear
  C)
                   \[{{68}^{o}}\]                    done clear
  D)
          \[{{106}^{o}}\] done clear
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