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NCERT Class 9 Mathematics Quadrilateral Formative Assessment Board Sample Problems
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
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 letีs 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
(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?
(a)
(b)
(c)
(d) None of these
Solution (a)
letีs 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?
(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 90 |
Isosceles trapezoid | A trapezoid having two right angles |
Trapezoid | Is a trapezoid whose non-parallel sides are equal |