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Class 9 Maths Important Questions for Quadilaterals




Given below are the Class 9 Maths Important Questions for Quadilaterals
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's
Question 1
Which are these is true or false about parallelogram
  1. The diagonals of a parallelogram bisect each other
  2. In a parallelogram, opposite sides and angle are equal.
  3. A diagonal of a parallelogram divides it into two congruent triangles
  4. The bisectors of the angles of parallelogram create a rectangle
  5. Sum of all the internal angles is 3600
  6. Sum of all the exterior angles is 1800
  7. Square, rectangle and rhombus are all parallelogram
  8. Consecutive angles are supplementary
Solution
  1. True. It is by definition
  2. True. It is by definition
  3. True. This can be proved easily using SSS congruence
  4. True
  5. True. This can easily proved by drawing one diagonal and summing all the angles based on triangle angle sum
  6. False
  7. True
  8. True
Question 2
True or False statement
  1. All the angles of the quadrilateral are obtuse
  2. Diagonal of the rhombus are equal and perpendicular to each other
  3. Diagonal of the square are equal and bisect each other at right angle
  4. Out of four points A,B,C,D in place, there are collinear. A quadrilateral can be formed from these points
  5. Trapezium, in which the sides that are not parallel are equal in length and angles formed by parallel sides are equal, such trapezium is called isosceles trapezium
  6. In a parallelogram, diagonal bisect the angles
Solution
  1. False
  2. false
  3. True
  4. False
  5. True
  6. True

Multiple choice Questions

Question 3
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD
Quadilateral Worksheets
Which of the following is true based on given information
a) AP=CQ
b) QD=PB
c) DP=QB
d) ΔPAD≅ ΔQCB
Solution
All are correct
In Triangle ΔPAD and ΔQCB
AD=CB
Angle P= Angle Q=900
∠CBQ=∠ADP Alternate interior angles of AB||CD
So AAS congruence
Also as they are congruent, we get AP=CQ and DP=QB
Now Lets see the triangles ?APB and ?CQD
AB=CD
Angle P= Angle Q=900
  Alternate interior angles of AB||CD
So QD=PB
Question 4
The angles of the quadrilateral are in the ratio 2:5:4:1?
Which of the following is true?
a)  Largest angle in the quadrilateral is 1500
b)  Smallest angle is 300
c)  The second largest angle in the quadrilateral is 800
d)  None of these
Solution (a) and (b)
Angles are 2x, 5x,4x,x
Now
2x+5x+4x+x=360
Or x=30
Angles are 30, 60,120,150
Question 5
Two adjacent angles in a parallelogram are in the ration 2:4. Find the values?
a) 80,100
b) 40,140
c) 60,120
d) None of the above
Solution (c)
Adjacent angles
2x+4x=180
x=30
60,120 are adjacent angles
Question 6
ABCD is a trapezium with AB =10cm, AD=5 cm, BC=4 cm and DC =7 cm?
Quadilateral Worksheets
Find the area of the ABCD
a)  34 cm2
b) 28cm2
c) 20 cm2
d) None of these
Solution (a)
BC is the altitude between the two parallel sides AB and DC
So Area of trapezium will be given by
A=(1/2)BC(AB+DC)=34cm2
Question 7
PQRS is a quadrilateral whose diagonal bisect each other at right angles
a) PQRS is a Square
b) PQRS is a rectangle
c) PQRS is a rhombus
d) None of these
Solution (c)
Question 8
ABCD is a trapezium where AB||DC. BD is the diagonal and E is the mid point of AD. A line is draw from point E parallel to AB intersecting BC at F. Which of these is true?
Quadilateral Worksheets a) BF=FC
b) EA=FB
c) CF=DE
d) None of these
Solution (a)
Let’s call the point of intersection at diagonal as G
Then in triangle DAB
EG||AB and E is the mid point of DA,So by converse of mid point theorem,
G is the mid point of BD
Now in triangle DBC
GF||CD
G is the mid point of DB
So by converse of mid point theorem
F is the mid point of BC
Question 9
 ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively
a) PQRS is a rectangle
b) PQRS is a parallelogram
c) PQRS is a rhombus
d) None of these
Solution (c)
Question 10
In a parallelogram PQRS, The bisector of angles P and Q meet at point O as shown in below figure. What is the angle O?
Quadilateral Worksheets a) 80
b) 90
c) 45
d) None of the above
Solution (b)

Match the column

Rhombus
Is a quadrilateral with only one pair of parallel sides.
Rectangles
Is a quadrilateral whose Two pairs of adjacent sides of a kite are equal, and one pair of opposite angles is equal. Diagonals intersect at right angles. One diagonal is bisected by the other.
Kite
Is a quadrilateral whose all the sides are equal and opposite sides are parallel. Opposite angles are equal.
Right-angled trapezoid
Is a quadrilateral whose opposite sides of a rectangle are parallel and equal. All angles are 90º.
Isosceles trapezoid
A trapezoid having two right angles
Trapezoid
Is a trapezoid whose non parallel sides are equal


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