9th Class Mathematics Quadrilaterals Question Bank

done Quadrilaterals Total Questions - 25

• question_answer1)
  The bisectors of angles of a parallelogram forms
  A)
   Trapezium         done clear
  B)
          Rectangle                      done clear
  C)
          Rhombus          done clear
  D)
          Kite                              done clear
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• question_answer2)
  If a quadrilateral has two adjacent sides are equal and the opposite sides are unequal, then it is called a                      
  A)
   Parallelogram                done clear
  B)
          Square                         done clear
  C)
          Rectangle          done clear
  D)
          Kite         done clear
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• question_answer3)
  If the angles of a quadrilateral are in the ratio 1: 2 : 3 ; 4. Then, the measure of  angles in descending order are         
  A)
   \[{{36}^{o}},\,\,{{108}^{o}},\,\,{{72}^{o}}\] and \[{{144}^{o}}\] done clear
  B)
         \[{{144}^{o}},\,\,{{108}^{o}},\,\,{{72}^{o}}\]and\[{{36}^{o}}\] done clear
  C)
         \[{{36}^{o}},\,\,{{72}^{o}},\,\,{{108}^{o}}\]and\[{{144}^{o}}\] done clear
  D)
          None of these                  done clear
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• question_answer4)
  In a\[\Delta ABC,P,Q\]and R are the mid-points of sides BC, CA and AB respectively. If AC =21 cm, BC=29cmandAB=30cm.The perimeter of the quadrilateral ARPQ \ is _____.     
  A)
   91 cm                          done clear
  B)
          60 cm              done clear
  C)
                      51 cm             done clear
  D)
          70cm                                                               done clear
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• question_answer5)
  The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If \[\angle DAC={{32}^{o}}\]and \[\angle AOB={{70}^{o}},\]then,\[\angle DBC\] is equal to ____.            
  A)
  \[{{38}^{o}}\] done clear
  B)
         \[{{86}^{o}}\] done clear
  C)
         \[{{24}^{o}}\] done clear
  D)
         \[{{32}^{o}}\] done clear
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• question_answer6)
                          If the angles of a quadrilateral are \[x+x+{{20}^{o}},x-{{40}^{o}}\]and\[2x.\]Then, the difference between greatest angle and the smallest angle is _____ .
  A)
  \[{{70}^{o}}\] done clear
  B)
                                 \[{{90}^{o}}\] done clear
  C)
         \[{{80}^{o}}\] done clear
  D)
          None of these    done clear
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• question_answer7)
  Two adjacent angles of a parallelogram are in the ratio 2 : 3. The angles are
  A)
  \[{{90}^{o}},\,\,{{180}^{o}}\] done clear
  B)
         \[{{36}^{o}},\,\,{{144}^{o}}\] done clear
  C)
         \[{{72}^{o}},\,\,{{108}^{o}}\] done clear
  D)
         \[{{52}^{o}},\,\,{{104}^{o}}\] done clear
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• question_answer8)
  In a quadrilateral ABCD, the line segments bisecting \[\angle C\]and \[\angle D\]meet at E. Then \[\angle A+\angle B\]is equal to _____.
  A)
  \[\angle CED\]                done clear
  B)
         \[\frac{1}{2}\angle CED\]            done clear
  C)
         \[2\angle CED\]               done clear
  D)
          None of these                done clear
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• question_answer9)
  The diagonals of a rectangle PQRS intersect at O. If \[\angle ROQ={{60}^{o}},\]then find \[\angle OSP.\]
  A)
  \[{{70}^{o}}\] done clear
  B)
         \[{{50}^{o}}\] done clear
  C)
         \[{{60}^{o}}\] done clear
  D)
         \[{{80}^{o}}\] done clear
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• question_answer10)
  If diagonals of a quadrilateral bisect each other at right angles, then it is a
  A)
   Parallelogram   done clear
  B)
          Rectangle          done clear
  C)
          Rhombus          done clear
  D)
          Trapezium         done clear
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• question_answer11)
  The measure of all the angles of a parallelogram, if an angle adjacent to the smallest angle is \[{{24}^{o}}\] less than twice the smallest angle, is
  A)
   \[{{37}^{o}},\,\,{{143}^{o}},\,\,{{37}^{o}},\,\,{{143}^{o}}\] done clear
  B)
         \[{{108}^{o}},\,\,{{72}^{o}},\,\,{{108}^{o}},\,\,{{72}^{o}}\] done clear
  C)
         \[{{68}^{o}},\,\,{{112}^{o}},\,\,{{68}^{o}},\,\,{{112}^{o}}\] done clear
  D)
          None of these done clear
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• question_answer12)
  The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle if
  A)
   PQRS is a rectangle done clear
  B)
          PQRS is a parallelogram done clear
  C)
          Diagonals of PQRS are equal done clear
  D)
          Diagonals of PQRS are at right angles done clear
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• question_answer13)
  ABCD is a rhombus with\[\angle ABC={{56}^{o}},\]then \[\angle ACD\]is equal to   
  A)
  \[{{90}^{o}}\] done clear
  B)
         \[{{60}^{o}}\] done clear
  C)
         \[{{56}^{o}}\] done clear
  D)
         \[{{62}^{o}}\] done clear
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• question_answer14)
  ABCD is a parallelogram. If AB is produced to E such that ED bisects BC at O. Then which of the following is correct?
  A)
   AB = OE       done clear
  B)
          AB = BE                      done clear
  C)
          OE = OC         done clear
  D)
          None of these    done clear
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• question_answer15)
  D and E are the mid-points of the sides AB and AC, respectively of \[\Delta ABC.DE\]is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
  A)
  \[\angle DAE=\angle EFC\]          done clear
  B)
          AE = EF          done clear
  C)
          DE = EF                      done clear
  D)
         \[\angle ADE=\angle ECF\]          done clear
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• question_answer16)
  X, Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD. AY and DX are joined intersecting in S; CX and BY are joined intersecting in R. Then SXRY is a
  A)
   Rectangle          done clear
  B)
          Rhombus                      done clear
  C)
          Parallelogram                done clear
  D)
          Square  done clear
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• question_answer17)
              In the given figure, if ABCD is a rectangle and P, Q are the mid-points of AD, DC respectively. Then, the ratio of lengths PQ and AC is equal to
  A)
   1 : 1                             done clear
  B)
          1 : 2                 done clear
  C)
          2 : 1                             done clear
  D)
          3 : 2     done clear
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• question_answer18)
  In given figure, ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that\[CQ=\frac{1}{4}AC\] and 4 PQ produced meet BC at R, then
  A)
  \[CR=\frac{1}{3}CB\]                done clear
  B)
          CR= RB          done clear
  C)
         \[CR=\frac{1}{2}RB\]                done clear
  D)
          None of these done clear
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• question_answer19)
  If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form
  A)
   Kite                              done clear
  B)
          Rhombus                      done clear
  C)
          Rectangle                      done clear
  D)
          Trapezium done clear
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• question_answer20)
  In figure, E and F are the mid-points of sides AB and AC of a\[\Delta ABC.\]If AB = 5 cm, BC = 5 cm     and AC = Q cm, then EF is equal to       
  A)
   3 cm                            done clear
  B)
          2.5 cm             done clear
  C)
          4 cm                            done clear
  D)
          None of these done clear
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• question_answer21)
  Study the statements carefully.

  Statement 1: If a sum of a pair of opposite angles of a quadrilateral is\[{{180}^{o}}\], the quadrilateral is cyclic.

  Statement 2: A line drawn through mid-point of a side of a triangle, parallel to another side equal to third side.

  Which of the following options holds?
  A)
   Both Statement-1 and Statement-2 are true. done clear
  B)
          Statement-1 is true but Statement-2 is false. done clear
  C)
          Statement-1 is false but Statement-2 is true. done clear
  D)
          Both Statement-1 and Statement-2 are false. done clear
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• question_answer22)
  Read the statements carefully and state ?T? for true and 'F' for false.

  (i) Diagonals of a parallelogram are perpendicular to each other.

  (ii) All four angles of a quadrilateral can be obtuse angles.

  (iii) If all sides of a quadrilateral are equal, then it is a rhombus.

  A)

  (i)	(ii)	(iii)
  T	F	F

                  done clear
  B)
        

  (i)	(ii)	(iii)
  F	F	T

                  done clear
  C)
                     done clear
  D)
        

  (i)	(ii)	(iii)
  F	F	F

  done clear
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• question_answer23)
  Fill in the blanks.

  (a) If consecutive sides of a parallelogram are equal then it is necessarily a P .

  (b) The figure formed by joining the mid-points of consecutive sides of a quadrilateral is Q .

  (c) If the diagonals of a parallelogram are equal and perpendicular to each other, it is a R .

  A)

  	P	Q	R
  	Square	Parallelogram	Rhombus

                  done clear
  B)
        

  	P	Q	R
  	Kite	Rhombus	Square

                  done clear
  C)
        

  	P	Q	R
  	Rhombus	Rectangle	Rectangle

                  done clear
  D)
        

  	P	Q	R
  	Rhombus	Parallelogram	Square

  done clear
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• question_answer24)
  If the sides BA and DC of quadrilateral  ABCD are produced as shown in the given figure, then
  A)
                      \[x+y=a+b\]                 done clear
  B)
         \[x-y=a-b\]        done clear
  C)
         \[\frac{x-y}{2}=a-b\]                 done clear
  D)
         \[2(x+y)=a+b\] done clear
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• question_answer25)
  By using a given figure of quadrilateral ABCD, match the following:

  	Column-I	Column-II
  (p)	(P) If ABCD is a  parallelogram, then sum of the angles  x, y and z is	(1) \[{{25}^{o}}\]
  (q)	(Q) If ABCD is a rhombus, where  \[\angle D={{130}^{o}},\]then the value of \[x\]is	(2) \[{{180}^{o}}\]
  (r)	(R) If ABCD is a  rhombus, the  value of w is	(3) \[{{50}^{o}}\]
  (s)	(S) If ABCD is a  parallelogram, where\[x+y={{130}^{o}}\]  then the value of B is	(4) \[{{90}^{o}}\]

  A)
  \[(p)\to (1),(q)\to (2),(r)\to (3),(s)\to (4)\] done clear
  B)
         \[(p)\to (2),(q)\to (1),(r)\to (4),(s)\to (3)\] done clear
  C)
         \[(p)\to (3),(q)\to (1),(r)\to (2),(s)\to (4)\] done clear
  D)
         \[(p)\to (4),(q)\to (3),(r)\to (1),(s)\to (2)\] done clear
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