Mathematics - Quadrilaterals
Exam Duration: 45 Mins Total Questions : 30
In the given figure, AO and DO are the bisectors of ∠A and ∠D of the quadrilateral ABCD. Find ∠AOD.
- (a)
67.5o
- (b)
77.5o
- (c)
87.5o
- (d)
99.75o
In a parallelogram find the sum of the bisected angles of two adjacent angles
- (a)
30o
- (b)
45o
- (c)
60o
- (d)
90o
The diameter of the circumcircle is the diagonal of a rectangle which is 10 cm and breadth of the rectangle is 6 cm. Find its length.
- (a)
6 cm
- (b)
5 cm
- (c)
8 cm
- (d)
7 cm
In a parallelogram ABCD, ∠D = 60o. Find the measure of ∠A.
- (a)
120o
- (b)
65o
- (c)
90o
- (d)
75o
In quadrilateral ABCD, if the diagonals AC and BD are equal and perpendicular to each other, what is ABCD
- (a)
A square
- (b)
A parallelogram
- (c)
A rhombus
- (d)
A trapezium
In a parallelogram ABCD, if AB = 2x + 5, CD = Y + 1, AD = Y + 5 and BC = 3x - 4, what is the ratio of AB and BC?
- (a)
71 : 21
- (b)
12: 11
- (c)
31 : 35
- (d)
4: 7
When is the quadrilateral formed by joining the midpoints of the sides of a quadrilateral PQRS, taken in order, a rectangle?
- (a)
PQRS is a rectanqle
- (b)
PQRSis a parallelogram
- (c)
Diagonals of PQRS are perpendicular.
- (d)
Diagonals of PQRSare equal
If ABCD is an isosceles trapezium, what is ∠C equal to?
- (a)
∠B
- (b)
∠A
- (c)
∠D
- (d)
90o
In a parallelogram ABCD, AB = 4 cm and BC= 7cm. Each of its diagonals is less than which of the following?
- (a)
3 cm
- (b)
4 cm
- (c)
7 cm
- (d)
11 cm
Which of the following is not a property of a rhombus
- (a)
All four sides are equal
- (b)
Diagonals bisect each other
- (c)
Diagonals bisect opposite angles
- (d)
One angle between the diagonals is 60o
In quadrilateral ABCD, ∠A = 38o, ∠C = 3 ∠A and ∠D = 4 ∠A. Find the value of ∠B.
- (a)
56o
- (b)
304o
- (c)
52o
- (d)
114o
In the given figure, p, q and r are three parallel lines. l and m are two transversals, such that DE = 1.5 cm, EF= 3 cm. Find BC if AB = 2.5 cm
- (a)
4 cm
- (b)
5.5 cm
- (c)
5 cm
- (d)
6 cm
Find the measure of each angle of a parallelogram, if one of its angles is 30o less than twice the smallest angle.
- (a)
70o,110o,70o,110o
- (b)
70o,110o,80o,100o
- (c)
120o,60o,120o,60o
- (d)
100o,80o,100o,80o
Which of the following pairs of angles are opposite angles of a cyclic quadrilateral?
- (a)
131o,28o
- (b)
95o,55o
- (c)
123o,57o
- (d)
64o,52o
Two adjacent angles of rhombus are 3x-40o and 2x + 20o.Find the measurement of the greater angle.
- (a)
160o
- (b)
100o
- (c)
80o
- (d)
120o
If the degree measures of the angles of a quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and the largest angle?
- (a)
140o
- (b)
150o
- (c)
168o
- (d)
180o
In a quadrilateral ABCD, diagonals bisect each other at right angles. If AB = BC = AD = 6 cm, find the length of CD
- (a)
3 cm
- (b)
6 cm
- (c)
6\(\sqrt { 2 } \) cm
- (d)
12 cm
In a quadrilateral three angles are in the ratio 3 : 3: 1 and the fourth angle is 80o. Find the measure of the other angles
- (a)
120o,120o,40o
- (b)
100o,100o,80o
- (c)
110o,110o,60o
- (d)
90o,90o,30o
Two angles of a quadrilateral are 60o are 70o and other two angles are in the ratio of 8: 15. Which of the following are the remaining two angles?
- (a)
80o,150o
- (b)
90o,140o
- (c)
100o,130o
- (d)
110o,120o
ABCD is a rhombus in which AC = 16 cm and BC = 10 cm. Find the length of the diagonal BD
- (a)
16 cm
- (b)
8 cm
- (c)
12 cm
- (d)
10 cm
In quadrilateral PQRS, ∠P + ∠R = 140o, and ∠Q : ∠S = 5 : 6. Find ∠Q.
- (a)
100o
- (b)
120o
- (c)
105o
- (d)
35o
E and F are the midpoints of the sides AB and AC respectively of \(\triangle \) ABC; G and H are midpoints of the sides AE and AF respectively of \(\triangle \)AEF.If GH = 1.8 cm, find BC.
- (a)
0.9 cm
- (b)
3.6 cm
- (c)
7.2 cm
- (d)
5.4 cm
If diagonals of a quadrilateral bisect each other at right angles, then it is a
- (a)
Parallelogram
- (b)
Rectangle
- (c)
Rhombus
- (d)
Trapezium
ABCD is a rhombus with \(\angle ABC\) = 56°, then \(\angle ACD\) is equal to
- (a)
90°
- (b)
60°
- (c)
56°
- (d)
62°
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
- (b)
AB = BE
- (c)
OE = OC
- (d)
None of these
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)
\(\angle DAE=\angle EFC\)
- (b)
AE = EF
- (c)
DE = EF
- (d)
\(\angle ADE=\angle ECF\)
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
- (b)
1: 2
- (c)
2: 1
- (d)
3: 2
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 - (b)
(i) (ii) (iii) F F T - (c)
(i) (ii) (iii) F T T - (d)
(i) (ii) (iii) F F F
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 - (b)
P Q R Kite Rhombus Square - (c)
P Q R Rhombus Rectangle Rectangle - (d)
P Q R Rhombus Parallelogram Square
By using a given figure of quadrilateral ABCD, match the following:
Column-I | Column-II |
---|---|
(P) If ABCD is a parallelogram, then sum of the angles x, y and z is | (1) 25o |
(Q) If ABeD is a rhombus, where \(\angle D\) = 130o, then the value of x is | (2) 180o |
(R) If ABCD is a rhombus the value of w is | (3) 50o |
(S) If ABCD is a parallelogram where x + y = 130o , then the value of \(\angle B\) is | (4) 90o |
- (a)
(P)\(\rightarrow\)(1), (Q)\(\rightarrow\)(2), (R)\(\rightarrow\)(3), (S)\(\rightarrow\)(4)
- (b)
(P)\(\rightarrow\)(2), (Q)\(\rightarrow\)(1), (R)\(\rightarrow\)(4), (S)\(\rightarrow\)(3)
- (c)
(P)\(\rightarrow\)(3), (Q)\(\rightarrow\)(1), (R)\(\rightarrow\)(2), (S)\(\rightarrow\)(4)
- (d)
(P)\(\rightarrow\)(4), (Q)\(\rightarrow\)(3), (R)\(\rightarrow\)(1), (S)\(\rightarrow\)(2)