7th Class Mental Ability The Triangle and its Properties Question Bank

done Properties of Triangles Total Questions - 40

• question_answer1)
  The angles of a triangle are  and \[{{(x-10)}^{o}}.\] What type of a triangle is it?
  A)
   An isosceles triangle                done clear
  B)
   A scalene triangle done clear
  C)
   A right angled triangle    done clear
  D)
   An equilateral triangle done clear
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• question_answer2)
  The angles of a triangle are in the ratio 1:3:5. Find the angles.
  A)
  \[60{}^\circ ,\text{ }40{}^\circ ,\text{ }80{}^\circ \] done clear
  B)
  \[20{}^\circ ,\text{ }60{}^\circ ,\text{ }100{}^\circ \] done clear
  C)
  \[30{}^\circ ,\text{ }90{}^\circ ,\text{ }50{}^\circ \] done clear
  D)
  \[30{}^\circ ,\text{ }60{}^\circ ,\text{ }90{}^\circ \]   done clear
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• question_answer3)
  Find the values of \[x\] and \[y\]in the figure given.
  A)
  \[x={{66}^{o}}\]    \[y=44{}^\circ \]                   done clear
  B)
  \[x={{44}^{o}}\]     \[~y=66{}^\circ \]    done clear
  C)
  \[x={{46}^{o}}\]     \[y=64{}^\circ \]                               done clear
  D)
  \[x={{64}^{o}}\]     \[y\text{ }=\text{ }46{}^\circ \]        done clear
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• question_answer4)
  From the following figure find the value of \[x.\]
  A)
  \[40{}^\circ \] done clear
  B)
  \[30{}^\circ \] done clear
  C)
  \[45{}^\circ \] done clear
  D)
  \[60{}^\circ \] done clear
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• question_answer5)
  \[\Delta ABC\]is isosceles and AB > AC. Which of the following must be false?
  A)
   AB = BC                    done clear
  B)
   BC = AC       done clear
  C)
        y = z               done clear
  D)
        x = z done clear
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• question_answer6)
  The diagonal of a rectangle is thrice its smaller side. Find the ratio of the length to the breadth of the rectangle.
  A)
   3 : 1                            done clear
  B)
  \[\sqrt{3}:1\]    done clear
  C)
       \[\sqrt{2}:1\]                done clear
  D)
       \[2\sqrt{2}:1\] done clear
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• question_answer7)
  In the given triangle, what is the value of z?
  A)
  \[65{}^\circ \] done clear
  B)
  \[35{}^\circ \] done clear
  C)
  \[55{}^\circ \] done clear
  D)
  \[90{}^\circ \] done clear
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• question_answer8)
  Two sides of a triangle are 7 units and 10 units.  Which of the following lengths can be the length of the third side?           
  A)
   2 units         done clear
  B)
               17 units           done clear
  C)
        13 units done clear
  D)
                    19 units done clear
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• question_answer9)
  In triangle EFG, EF = FG = EG = 7.5 cm. What is the measure of\[\angle FEG?\]
  A)
  \[60{}^\circ \] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[36{}^\circ \] done clear
  D)
  \[120{}^\circ \] done clear
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• question_answer10)
  In \[\Delta ABC,3\angle A=2\angle B\]and \[2\angle A=\angle C.\] Find the angles of the triangle

  \[\angle A\]

  \[\angle B\]

  \[\angle C\]

                 
  A)

  \[{{40}^{o}}\]

  \[{{80}^{o}}\]

  \[{{60}^{o}}\]

                  done clear
  B)

  \[{{60}^{o}}\]

  \[{{40}^{o}}\]

  \[{{80}^{o}}\]

                  done clear
  C)

  \[{{60}^{o}}\]

  \[{{80}^{o}}\]

  \[{{40}^{o}}\]

                  done clear
  D)

  \[{{40}^{o}}\]

  \[{{60}^{o}}\]

  \[{{80}^{o}}\]

  done clear
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• question_answer11)
  \[\Delta ABC\]is right angled at B. Which statement is true?
  A)
  \[x+y={{180}^{o}}\]       done clear
  B)
       \[~x+y=270{}^\circ \]         done clear
  C)
       \[~x+y=300{}^\circ \]       done clear
  D)
       \[~x+y=90{}^\circ \]                       done clear
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• question_answer12)
  In an isosceles triangle ABC, with AB = AC, BD is perpendicular from B to the side AC. What is the value of \[B{{D}^{2}}-C{{D}^{2}}?\]
  A)
   2AB.BC          done clear
  B)
                    2AD.BD          done clear
  C)
   2 DC.AD        done clear
  D)
        2 BD.CD done clear
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• question_answer13)
  In the figure, ACE and BCD are straight lines. Given that AB = BC = CA, find \[\angle CED.\]
  A)
  \[{{100}^{o}}\]                    done clear
  B)
       \[{{120}^{o}}\]        done clear
  C)
        \[{{60}^{o}}\]                     done clear
  D)
       \[{{30}^{o}}\] done clear
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• question_answer14)
  In \[\Delta ABC,AB=BC\]and \[\overline{BD}\]bisects \[\overline{AC}.\] Which of the following cannot be concluded?
  A)
  \[AD=DC\]           done clear
  B)
      \[~w=z\]         done clear
  C)
       \[x=y\]               done clear
  D)
       \[~w=x\]         done clear
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• question_answer15)
  Find the length of diagonal of a square whose area is\[~78400\text{ }c{{m}^{2}}.\]
  A)
  \[280\sqrt{2}\] done clear
  B)
       \[28\sqrt{2}\,cm\]        done clear
  C)
       \[280cm\]         done clear
  D)
       \[280\sqrt{3}\,cm\]                  done clear
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• question_answer16)
  In a triangle ABC, AB + BC = 10 cm; BC + CA = 12 cm and CA + AB = 16 cm. Find the perimeter of the triangle.                                   
  A)
   38 cm            done clear
  B)
                    19 cm done clear
  C)
        76 cm            done clear
  D)
                    36 cm done clear
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• question_answer17)
  What is the height of an equilateral triangle if one of its sides is 10 cm long?
  A)
  \[\sqrt{2}\,cm\]                        done clear
  B)
  \[3\sqrt{5}\,cm\]          done clear
  C)
       \[3\sqrt{2}\,cm\]          done clear
  D)
       \[5\sqrt{3}\,cm\] done clear
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• question_answer18)
  In \[\Delta ABC,\angle B\]is a right angle, AC = 24 cm, D is the mid point of AC. Find the length of BD.
  A)
   24 cm               done clear
  B)
        12 cm done clear
  C)
        6 cm                done clear
  D)
        7 cm done clear
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• question_answer19)
  In\[\Delta ABC,BC=AC\]and\[\angle B={{72}^{o}},\]find the measures of \[\angle A\]and \[\angle C.\]
  A)
  \[\angle A={{72}^{o}},\angle C={{36}^{o}}\]               done clear
  B)
  \[\angle A={{36}^{o}},\angle C={{36}^{o}}\] done clear
  C)
  \[\angle A={{72}^{o}},\angle C={{48}^{o}}\]               done clear
  D)
  \[\angle A={{42}^{o}},\angle C={{66}^{o}}\] done clear
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• question_answer20)
  One of the exterior angles of a triangle is 120° and the interior opposite angles are in the ratio 1 : 5. Find the angles of the triangle.

  \[\angle A\]

  \[\angle B\]

  \[\angle C\]

                 
  A)

  \[{{100}^{o}}\]

  \[{{20}^{o}}\]

  \[{{60}^{o}}\]

  done clear
  B)

  \[{{100}^{o}}\]

  \[{{60}^{o}}\]

  \[{{20}^{o}}\]

                  done clear
  C)

  \[{{20}^{o}}\]

  \[{{60}^{o}}\]

  \[{{100}^{o}}\]

                  done clear
  D)

  \[{{60}^{o}}\]

  \[{{20}^{o}}\]

  \[{{100}^{o}}\]

  done clear
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• question_answer21)
  What is the measure of \[x\] in the given figure?
  A)
   17 cm             done clear
  B)
        15 cm                         done clear
  C)
   12 cm             done clear
  D)
        16 cm done clear
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• question_answer22)
  In the given figure, if z = 30°, what is the value of \[x+y?\]
  A)
   \[{{60}^{o}}\]                                 done clear
  B)
  \[{{210}^{o}}\]                    done clear
  C)
   \[{{330}^{o}}\]       done clear
  D)
       \[{{150}^{o}}\] done clear
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• question_answer23)
  In\[\Delta PQR,\angle P-\angle Q={{18}^{o}}\]and \[\angle Q-\angle R={{12}^{o}}.\]Find all the angles of the triangle.

  \[\angle P\]

  \[\angle Q\]

  \[\angle R\]

                 
  A)

  \[{{76}^{o}}\]

  \[{{46}^{o}}\]

  \[{{58}^{o}}\]

                  done clear
  B)

  \[{{46}^{o}}\]

  \[{{58}^{o}}\]

  \[{{76}^{o}}\]

                  done clear
  C)

  \[{{76}^{o}}\]

  \[{{58}^{o}}\]

  \[{{46}^{o}}\]

  done clear
  D)

  \[{{46}^{o}}\]

  \[{{76}^{o}}\]

  \[{{58}^{o}}\]

  done clear
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• question_answer24)
  If the sides of a right triangle are\[x,x+1\]and \[x-1,\]what is the measure of its hypotenuse?
  A)
   5                                 done clear
  B)
   4        done clear
  C)
        1                     done clear
  D)
        0 done clear
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• question_answer25)
  A man goes 150 m due east and then 200 m due north. How far is he from the starting point?
  A)
   180 m             done clear
  B)
        280 m             done clear
  C)
        160 m             done clear
  D)
        250 m done clear
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• question_answer26)
  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 smallest side. 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_answer27)
  A rectangular carpet has an area of 60 sq. m. If its diagonal and longer side together equal 5 times the shorter side, find the length of the carpet.
  A)
   5 m                 done clear
  B)
        12 m               done clear
  C)
        13 m               done clear
  D)
        14.5 m done clear
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• question_answer28)
  Observe the given triangle. Which of the following is true about t, r and\[x?\]
  A)
  \[~t<x<r\]                  done clear
  B)
  \[~r<t<x~~\]           done clear
  C)
       \[~x<t<r\]      done clear
  D)
       \[~t<r<x\] done clear
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• question_answer29)
  In the given figure, what is the value of 'c' in terms of 'a' and 'b'?       
  A)
  \[180{}^\circ \text{ }-\text{ }a-b~\]              done clear
  B)
  \[a+3b-180{}^\circ \] done clear
  C)
  \[360{}^\circ -2a-3b\] done clear
  D)
  \[2(a+b-90{}^\circ )\] done clear
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• question_answer30)
  Identify the false statement.
  A)
   The difference of two sides of a triangle is lesser than its third side. done clear
  B)
   A triangle can have an obtuse angle and a right angle. done clear
  C)
   The angle opposite to the smallest side of a triangle is the least. done clear
  D)
   All of the above. done clear
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• question_answer31)
  In the figure given, if T is the midpoint of \[\overline{QR},\]and\[\overline{PT}\]is perpendicular to\[\overline{QR},\]what is the length of\[\overline{PT}?\]
  A)
   10 cm                         done clear
  B)
   15 cm             done clear
  C)
        20 cm             done clear
  D)
        25 cm             done clear
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• question_answer32)
  BCD and BEA are straight lines. Find \[\angle x.\]
  A)
  \[28{}^\circ \] done clear
  B)
  \[86{}^\circ \] done clear
  C)
  \[76{}^\circ \] done clear
  D)
  \[104{}^\circ \] done clear
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• question_answer33)
  If one angle of a triangle is greater than each of the two remaining angles by \[30{}^\circ \], find the angles of the triangle.
  A)
  \[40{}^\circ ,\text{ }40{}^\circ ,\text{ }100{}^\circ \] done clear
  B)
  \[50{}^\circ ,\text{ }50{}^\circ ,\text{ }80{}^\circ \] done clear
  C)
  \[30{}^\circ ,\text{ }30{}^\circ ,\text{ }120{}^\circ \] done clear
  D)
    \[35{}^\circ ,\text{ }35{}^\circ ,\text{ }110{}^\circ \]   done clear
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• question_answer34)
  A builder constructed a ramp to take material to the top of a building 12 m high. The distance between the foot of the ramp and the foot of the wall is 35 m. What is the length of the ramp?
  A)
   26 m               done clear
  B)
        36 m               done clear
  C)
        46 m               done clear
  D)
        37 m done clear
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• question_answer35)
  ABC is a triangle in which BC is produced to D, CA is produced to\[\angle DCA={{108}^{o}},\]and \[\angle EAB={{124}^{o}}.\]What is the measure of \[\angle ABC?\]
  A)
  \[{{58}^{o}}\]                                  done clear
  B)
   \[{{52}^{o}}\] done clear
  C)
   \[{{72}^{o}}\] done clear
  D)
   \[{{68}^{o}}\] done clear
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• question_answer36)
  If A : An isosceles triangle is right angled. \[R:\angle A=\angle B={{45}^{o}}\]and \[\angle C={{90}^{o}}.\]Which of the following statements can be true?
  A)
   A is true and R is the correct explanation of A. done clear
  B)
   A is true and R is not the correct explanation of A. done clear
  C)
   A is false. done clear
  D)
   R is false. done clear
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• question_answer37)
  If the angles of a triangle are \[{{(2x+5)}^{o}},{{(x+20)}^{o}}\] and\[{{(2x-10)}^{o}},\]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)
   An isosceles triangle done clear
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• question_answer38)
  A ship sails 33 km due south, and then 56 km due west. How far is it from its starting point?
  A)
   68 km                         done clear
  B)
   56 km             done clear
  C)
   65 km             done clear
  D)
        58 km done clear
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• question_answer39)
  In the figure given, \[\Delta ABC\] is right triangle and \[\angle ={{40}^{o}}.\] What is the measure of\[\angle ECD?\]
  A)
  \[40{}^\circ \]          done clear
  B)
  \[50{}^\circ \] done clear
  C)
  \[130{}^\circ \] done clear
  D)
  \[140{}^\circ \] done clear
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• question_answer40)
  Which of the following are 2 of the 3 interior angle measurements of a triangle for which the 3rd angle is the same as one of the two given measurements?
  A)
  \[20{}^\circ ,\text{ }40{}^\circ \] done clear
  B)
  \[40{}^\circ ,\text{ }30{}^\circ \] done clear
  C)
  \[100{}^\circ ,\text{ }40{}^\circ \] done clear
  D)
  \[50{}^\circ ,\text{ }60{}^\circ \] done clear
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