7th Class Mathematics The Triangle and its Properties Question Bank

done Properties of Triangle Total Questions - 40

• question_answer1)
  Which of the following sets of measures cannot be the lengths of the sides of a right triangle?
  A)
   5 cm, 4 cm and 03 cm            done clear
  B)
   8 cm, 6 cm and 11 cm done clear
  C)
   1 cm, \[2.4\]cm and \[2.6\] cm         done clear
  D)
   60 cm, 25 cm and 65 cm done clear
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• question_answer2)
  In a \[\Delta PQR,\] If\[P{{Q}^{2}}=P{{R}^{2}}+Q{{R}^{2}},\]at which vertex is the right angle?
  A)
   P                                 done clear
  B)
   Q              done clear
  C)
   R                     done clear
  D)
   Either P or Q done clear
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• question_answer3)
  The given figure shows a right-angled \[\Delta PQR.\]Each of the three sides of the triangle also act as sides of a square. What is the area of the shaded region in the given figure?
  A)
   \[9\text{ }c{{m}^{2}}\]                               done clear
  B)
   \[\text{13 }c{{m}^{2}}\]        done clear
  C)
   \[\text{26 }c{{m}^{2}}\]        done clear
  D)
   \[\text{18 }c{{m}^{2}}\] done clear
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• question_answer4)
  Which type of triangle is formed by \[BC=7.2\text{ }cm,\text{ }AC=6\text{ }cm\] and \[\angle C=120{}^\circ \]?
  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_answer5)
  What is the perimeter of the given figure?
  A)
   12                               done clear
  B)
   14 done clear
  C)
   \[16.6\]                        done clear
  D)
   \[18.2\] done clear
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• question_answer6)
  Which triangle is formed by \[AB=5\text{ }cm,\text{ }BC=6\text{ }cm\] and \[AC=7\text{ }cm\]?
  A)
   A scalene triangle.        done clear
  B)
   An isosceles triangle. done clear
  C)
   An equilateral triangle             done clear
  D)
   none of above done clear
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• question_answer7)
  The length of one of the diagonals of a rhombus is\[4\text{ }cm\]. If each side of the rhombus measures \[2.5\text{ }cm,\] then what is the length of the other diagonal?
  A)
   5 cm                           done clear
  B)
   6 cm          done clear
  C)
   \[3.5\text{ }cm\]                      done clear
  D)
   \[3\text{ }cm\] done clear
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• question_answer8)
  If two angles in a triangle are \[55{}^\circ \] and \[45{}^\circ ,\] what is the third angle?
  A)
   \[80{}^\circ \]                           done clear
  B)
   \[55{}^\circ \]            done clear
  C)
   \[45{}^\circ \]                           done clear
  D)
   \[90{}^\circ \] done clear
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• question_answer9)
  The given figure shows two buildings AB and CD. X is a point between the buildings from which two ropes are tied without slack to the top of the buildings. What is the distance between the buildings?
  A)
   \[15\,m\]                     done clear
  B)
   \[14\,m\]          done clear
  C)
   \[13\,m\]                      done clear
  D)
   \[12\,m\] done clear
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• question_answer10)
  If one angle is the average of the other two angles and the difference between the greatest and least angles is \[60{}^\circ ,\] 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_answer11)
  If two angles of a triangle measure \[45{}^\circ \] and \[60{}^\circ ,\]then which of the following angle cannot be the measure of one of the exterior angles of the triangle?
  A)
   \[105{}^\circ \]                         done clear
  B)
   \[120{}^\circ \]           done clear
  C)
   \[140{}^\circ \]              done clear
  D)
   \[135{}^\circ \] done clear
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• question_answer12)
  In \[\Delta ABC,\]If \[AB=BC\] and \[\angle B=40{}^\circ ,\]what is the measure of \[\angle C\]?
  A)
  \[70{}^\circ \]          done clear
  B)
   \[80{}^\circ \]            done clear
  C)
   \[130{}^\circ \]                         done clear
  D)
   \[40{}^\circ \] done clear
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• question_answer13)
  The given figure shows two parallel lines AB and CD, which are intersected by transversal PQ at L and M. LD is also joined as shown. What is the value of x in the given figure?
  A)
   \[63{}^\circ \]                           done clear
  B)
   \[58{}^\circ \]            done clear
  C)
   \[70{}^\circ \]            done clear
  D)
   \[85{}^\circ \] done clear
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• question_answer14)
  Which triangle is formed by \[BC=AC=4.8\text{ }cm\] and \[\angle C=90{}^\circ ?\]
  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_answer15)
  What is the value of \[\angle a\] in the given figure?
  A)
   \[145{}^\circ \]                         done clear
  B)
   \[125{}^\circ \]         done clear
  C)
   \[100{}^\circ \]                     done clear
  D)
   \[140{}^\circ \] done clear
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• question_answer16)
  Which of the following statement is true?
  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 shortest side. done clear
  C)
   A, B and C are not collinear if \[AB+BC=AC\]. done clear
  D)
   The sum of angles in a triangle is less than\[180{}^\circ \]. done clear
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• question_answer17)
  \[AB||CD\] in the figure as shown below, then \[~\angle ACD\] is equal to
  A)
   \[80{}^\circ \]                           done clear
  B)
   \[40{}^\circ \]            done clear
  C)
   \[60{}^\circ \]               done clear
  D)
   \[65{}^\circ \] done clear
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• question_answer18)
  What is the length of the hypotenuse of a right angled triangle whose two legs measure \[30\text{ }cm\] and \[0.4\] metres.
  A)
   50 cm             done clear
  B)
   60 cm          done clear
  C)
   \[0.568\text{ }cm\]                  done clear
  D)
   37 cm done clear
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• question_answer19)
  The three angles of a triangle are in the ratio \[1:2:3,\] then the greatest angle is
  A)
   \[105{}^\circ \]                         done clear
  B)
   \[90{}^\circ \]           done clear
  C)
   \[120{}^\circ \]                     done clear
  D)
   \[100{}^\circ \] done clear
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• question_answer20)
  If the two legs of a right angled triangle are equal and the square of the hypotenuse is \[400\text{ }sq\text{ }cm,\]what is the length of each leg?
  A)
   \[40\text{ }cm\]                       done clear
  B)
   \[\text{10}\sqrt{2}\text{ }cm\]     done clear
  C)
   \[\text{50}\sqrt{2}\text{ }cm\]           done clear
  D)
   15 cm done clear
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• question_answer21)
  If one of the angles of an isosceles triangle measures \[30{}^\circ ,\] then what are the possible differences between the measures of its unequal angles?
  A)
   \[20{}^\circ \]and \[70{}^\circ \]                done clear
  B)
   \[45{}^\circ \] and \[90{}^\circ \]     done clear
  C)
   \[30{}^\circ \]and \[90{}^\circ \]                done clear
  D)
   \[45{}^\circ \]and \[105{}^\circ \] done clear
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• question_answer22)
  If two sides of an isosceles triangle are 4 cm and 9 cm, what is the length of the third side?
  A)
   4 cm                           done clear
  B)
   9 cm         done clear
  C)
   4 cm or 9 cm      done clear
  D)
   12 cm done clear
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• question_answer23)
  The given figure shows an isosceles \[\Delta ABC\] with\[AB=BC\]. Sides BC and AC are extended to S and T respectively, such that CS and CT along with ST form sides of \[\Delta CST\]. How can \[\Delta CST\] be classified
  A)
   Acute - angled and scalene          done clear
  B)
   Acute - angled and isosceles done clear
  C)
   Right - angled and scalene          done clear
  D)
   Right - angled and isosceles done clear
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• question_answer24)
  In a \[\Delta ABC\] if \[AB+BC=8\text{ }cm,\] \[BC+CA=10\text{ }cm,\] \[CA+AB=12\text{ }cm,\] what is the sum of the lengths of its sides?
  A)
   15 cm             done clear
  B)
   20cm         done clear
  C)
   \[37.5\text{ }cm\]                    done clear
  D)
   40 cm done clear
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• question_answer25)
  \[\Delta ABC\] is right - angled at B. If the measures of \[\angle A\] and \[\angle C\] are in the ratio \[7:5\] then what is the measure of \[\angle C\]?
  A)
   \[40{}^\circ \]                           done clear
  B)
   \[60{}^\circ \] done clear
  C)
   \[37.5{}^\circ \]            done clear
  D)
   \[70{}^\circ \] done clear
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• question_answer26)
  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)
   none of these done clear
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• question_answer27)
  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_answer28)
  If the angles of a triangle are in the ratio \[1:3:14\] 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_answer29)
  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_answer30)
  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_answer31)
  In a \[\Delta \text{ }ABC,\]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_answer32)
  Two chimneys 18 m and 13 m high stand upright on a ground. If their feet are 12 m apart, what is the distance between their tops?
  A)
   10 cm                         done clear
  B)
   27 m          done clear
  C)
   13 m      done clear
  D)
   9 m done clear
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• question_answer33)
  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)
   18 m                           done clear
  B)
   25 m       done clear
  C)
   27 m               done clear
  D)
   29 m done clear
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• question_answer34)
  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_answer35)
  The centroid of a triangle is the point or 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_answer36)
  Which of the following statements is false?
  A)
   The centroid of an acute angled triangle lies in the interior of the triangle. done clear
  B)
   The orthocenter 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)
   From cicumcenter, we cannot draw a circle touching all the three vertices of triangle. done clear
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• question_answer37)
  Which of the following statements is false?
  A)
   The orthocenter 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)
   Incentre lies outside then triangle. done clear
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• question_answer38)
  In \[\Delta PQR,\text{ }PQ\text{ }=\text{ }PR;\]M is a mid point on QR and \[MT\bot QR\]. What do you call MT?
  A)
   Centroid                     done clear
  B)
   Median         done clear
  C)
   Perpendicular bisector            done clear
  D)
   Vertex done clear
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• question_answer39)
  Which of the following statements is NOT true?
  A)
   A triangle can not have two obtuse angles. done clear
  B)
   A triangle can have three acute angles. 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)
  Find the angles x and y respectively, \[BE||DC\]
  A)
   \[x=30{}^\circ ,\text{ }y=50{}^\circ \]                   done clear
  B)
   \[x=25{}^\circ ,\text{ }y=75{}^\circ \] done clear
  C)
   \[x=50{}^\circ ,y=30{}^\circ \]        done clear
  D)
   \[x=50{}^\circ ,y=25{}^\circ \] done clear
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