Given below are the Class 9 Maths Important Questions for Quadrilaterals
a. Concepts questions
b. Calculation problems
c. Multiple choice questions
d. Long answer questions
e. Fill in the blanks
Question 1
Which are these is true or false about parallelogram
- The diagonals of a parallelogram bisect each other
- In a parallelogram, opposite sides and angle are equal.
- A diagonal of a parallelogram divides it into two congruent triangles
- The bisectors of the angles of parallelogram create a rectangle
- Sum of all the internal angles is 3600
- Sum of all the exterior angles is 1800
- Square, rectangle and rhombus are all parallelogram
- Consecutive angles are supplementary
Check your Answer
- True. It is by definition
- True. It is by definition
- True. This can be proved easily using SSS congruence
- True
- True. This can easily proved by drawing one diagonal and summing all the angles based on triangle angle sum
- False
- True
- True
Question 2
True or False statement
- All the angles of the quadrilateral are obtuse
- Diagonal of the rhombus are equal and perpendicular to each other
- Diagonal of the square are equal and bisect each other at right angle
- Out of four points A,B,C,D in place, there are collinear. A quadrilateral can be formed from these points
- 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
- In a parallelogram, diagonal bisect the angles
Check your Answer
- False
- false
- True
- False
- True
- True
Multiple choice Questions
Question 3
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD
Which of the following is true based on given information
a. $AP=CQ$
b. $QD=PB$
c. $DP=QB$
d. $\Delta PAD \cong \Delta QCB$
Solution
All are correct
In Triangle $ \Delta PAD \; and \; \Delta QCB$
AD=CB
$\angle P= \angle Q=90^0$
$\angle CBQ=\angle ADP$ ( 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 $\Delta APB \; and \; \Delta CQD$
AB=CD
$\angle P= \angle Q=90^0$ (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 $150^0$
b. Smallest angle is $30^0$
c.The second largest angle in the quadrilateral is $80^0$
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 $30^0, 60^0,120^0,150^0$
Question 5
Two adjacent angles in a parallelogram are in the ratio 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?
Find the area of the ABCD
a. 34 cm
2
b. 28cm
2
c. 20 cm
2
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
$A=\frac {1}{2}BC(AB+DC)=34cm^2$
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?
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?
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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