NCERT Class 9 Mathematics Quadrilateral Formative Assessment Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 1

Which are these is true or false about parallelogram

(a) The diagonals of a parallelogram bisect each other

(b) In a parallelogram, opposite sides and angle are equal.

(c) A diagonal of a parallelogram divides it into two congruent triangles

(d) The bisectors of the angles of parallelogram create a rectangle

(e) Sum of all the internal angles is

(f) Sum of all the exterior angles is

(g) Square, rectangle and rhombus are all parallelogram

(h) Consecutive angles are supplementary

Solution

(a) True. It is by definition

(b) True. It is by definition

(c) True. This can be proved easily using SSS congruence

(d) True

(e) True. This can easily proved by drawing one diagonal and summing all the angles based on triangle angle sum

(f) False

(g) True

(h) True

Question 2

True or False statement

(a) All the angles of the quadrilateral are obtuse

(b) Diagonal of the rhombus are equal and perpendicular to each other

(c) Diagonal of the square are equal and bisect each other at right angle

(d) Out of four points A, B, C, D in place, there are collinear. A quadrilateral can be formed from these points

(e) 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

(f) In a parallelogram, diagonal bisect the angles

Solution

(a) False

(b) False

(c) True

(d) False

(e) True

(f) True

Multiple choice Questions

Question 3

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal

BD

ABCD is a Parallelogram

Which of the following is true based on given information

a)

b)

c)

d)

Solution

All are correct

In Triangle and

Angle P = Angle

Alternate interior angles of

So AAS congruence

Also as they are congruent, we get and

Now let՚s see the triangles and

Angle P = Angle

Alternate interior angles of

So

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

b) Smallest angle is

c) The second largest angle in the quadrilateral is

d) None of these

Solution (a) and (b)

Angles are

Now

Or

Angles are

Question 5

Two adjacent angles in a parallelogram are in the ration 2: 4. Find the values?

a)

b)

c)

d) None of the above

Solution (e)

Adjacent angles

are adjacent angles

Question 6

ABCD is a trapezium with and ?

Find the area of the ABCD

ABCD is a Trapezium

a)

b)

c)

d) None of these

Solution (a)

B

BC is the altitude between the two parallel sides AB and DC

So Area of trapezium will be given by

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 . BD is the diagonal and E is the midpoint of AD. A line is draw from point E parallel to AB intersecting BC at F. Which of these is true?

ABCD is a Trapezium Where AB‖DC

a)

b)

c)

d) None of these

Solution (a)

let՚s call the point of intersection at diagonal as G

Then in triangle DAB

and E is the midpoint of DA, So by converse of mid point theorem,

G is the midpoint of BD

Now in triangle DBC

G is the midpoint of DB

So by converse of mid-point theorem

F is the midpoint 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?

The Bisector of Angles P and Q

a) 80

b) 90

c) 45

d) None of the above

Solution (b)

Match the column

Table Supporting: NCERT Class 9 Mathematics Quadrilateral Formative Assessment Board Sample Problems
RhombusIs a quadrilateral with only one pair of parallel sides?
RectanglesIs 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.
KiteIs a quadrilateral whose all the sides are equal and opposite sides are parallel. Opposite angles are equal.
Right-angled trapezoidIs a quadrilateral whose opposite sides of a rectangle are parallel and equal? All angles are 90
Isosceles trapezoidA trapezoid having two right angles
TrapezoidIs a trapezoid whose non-parallel sides are equal