Olympiad Mathematics - Understanding Quadrilaterals
Exam Duration: 45 Mins Total Questions : 25
ABCD is a rhombus in which the altitude from D to side AB bisects AB. Then ㄥA and ㄥB respectively, are ______
- (a)
60°, 120°
- (b)
120°, 60°
- (c)
80°, 100°
- (d)
100°, 80°
The exterior angle of a regular polygon is one-third of its interior angle. How many sides does the polygon has?
- (a)
10
- (b)
8
- (c)
9
- (d)
13
If the diagonals of a quadrilateral bisect each other at right angle, then it is a ______
- (a)
Kite
- (b)
Parallelogram
- (c)
Rhombus
- (d)
Rectangle
The number of sides of a regular polygon whose each exterior angle has a measure of 30° is ______
- (a)
12
- (b)
6
- (c)
8
- (d)
10
In the given figure, the value of x is ________
- (a)
120°
- (b)
140°
- (c)
160°
- (d)
130°
If each pair of opposite sides of a quadrilateral are equal and parallel, then it is a ______
- (a)
Kite
- (b)
Trapezium
- (c)
Parallelogram
- (d)
None of these
The given quadrilateral EFGH is a ________
- (a)
Parallelogram
- (b)
Concave quadrilateral
- (c)
Convex quadrilateral
- (d)
Trapezium
The ratio of two sides of a parallelogram is 3:5 and its perimeter is 48 cm. Then, the sides of the parallelogram are ______
- (a)
9 cm, 16 cm
- (b)
9 cm, 15 cm
- (c)
8 cm, 15 cm
- (d)
6 cm, 10 cm
In the given figure, line RT is drawn parallel to SQ. If ㄥQPS = 100°, ㄥPQS = 40°, ㄥPSR = 85° and ㄥQRS = 70°, then ㄥQRT= ________
- (a)
45°
- (b)
65°
- (c)
85°
- (d)
90°
Which of the quadrilaterals is NOT a parallelogram?
- (a)
Rectangle
- (b)
Square
- (c)
Kite
- (d)
Rhombus
Which of the following statements is CORRECT?
- (a)
The diagonals of a parallelogram are equal
- (b)
The diagonals of a rectangle are perpendicular to each other
- (c)
If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus.
- (d)
Every quadrilateral is either a trapezium or a parallelogram or a kite.
Four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The difference between the greatest and the smallest angle is _______
- (a)
125°
- (b)
75°
- (c)
108°
- (d)
120°
A trapezium in which non-parallel sides are equal is said to be ________
- (a)
Right trapezium
- (b)
Equilateral trapezium
- (c)
Isosceles trapezium
- (d)
None of these
Which of the following can never be the measure of exterior angle of a regular polygon?
- (a)
22°
- (b)
36°
- (c)
45°
- (d)
30°
The quadrilateral having only one pair of opposite sides parallel is called a ______
- (a)
Square
- (b)
Rhombus
- (c)
Trapezium
- (d)
Parallelogram
The theatre in the town is built in the form of a kite. Its perimeter is 100 m. If one of : its sides is 20 m, then what are the lengths . of other sides?
- (a)
20 m, 30 m, 30 m
- (b)
30 m, 40 m, 40 m
- (c)
20 m, 40 m, 32 m
- (d)
30 m, 40 m, 50 m
Vikas's garden is in the form of a parallelogram whose one side is 4.8 cm and other side is 1\(\frac{1}{2}\) times of this side. He wants to fence his garden four times by a wire. Find the length of the wire required.
- (a)
96 cm
- (b)
108 cm
- (c)
132 cm
- (d)
84 cm
A field is in the form of an isosceles trapezium whose perimeter is 215 m. One of its non-parallel side is 50 m. What is the sum of its parallel sides?
- (a)
115 m
- (b)
60 m
- (c)
165 m
- (d)
135 m
Rohit has 6 wooden sticks of equal length. He wants to join all of them in such a way that they make a regular polygon. At what internal angle he has to join wooden stick with each other?
- (a)
105°
- (b)
120°
- (c)
115°
- (d)
90°
Atul is playing in a playground which is of the form of a parallelogram. He observes that the diagonals of the playground are 80 m and 60 m long. So, the playground is in the shape of ________
- (a)
Rectangle
- (b)
Rhombus
- (c)
Kite
- (d)
Square
Match the following:
Column-I | Column-II |
(P) Diagonals of a rectangle | (1) Bisect each other at right angles |
(Q) Diagonals of a square | (2) Bisect each other |
(R) Diagonals of a rhombus | (3) Equal and bisect each other |
(S) Diagonals of a parallelogram. | (4) Equal and bisect each other at right angles |
- (a)
(P) ⟶ (1), (Q) ⟶ (2), (R) ⟶ (3), (S) ⟶ (4)
- (b)
(P) ⟶ (3), (Q) ⟶ (4), (R) ⟶ (1), (S) ⟶ (2)
- (c)
(P) ⟶ (4), (Q) ⟶ (2), (R) ⟶ (3), (S) ⟶ (1)
- (d)
(P) ⟶ (4), (Q) ⟶ (3), (R) ⟶ (2), (S) ⟶ (1)
In the given figure (not drawn to scale), DO and CO are the bisectors of ㄥADC and ㄥBCD respectively. If ㄥADC = ㄥBCD = 60° and ㄥDAB = 100°, find the measure of ㄥDOC and ㄥABC respectively.
- (a)
100°, 160°
- (b)
110°, 150°
- (c)
120°, 140°
- (d)
110°, 130°
Fill in the blanks.
(i) Sum of interior angles of a polygon of n sides is P right angles.
(ii) The measure of at least one Q angle of a concave quadrilateral is more than 180°.
(iii) A quadrilateral which has only one pair of equal opposite angles is L.
(iv) Sum of all exterior angles of a polygon of n sides is S.
- (a)
P Q R S 4 exterior kite n x 3600 - (b)
P Q R S n-2 exterior trapezium n x 1800 - (c)
P Q R S 2n-4 interior trapezium 3600 - (d)
P Q R S 2 interior trapezium 1800
ABCD is a parallelogram. Find the angles x, y and z in the given figure.
- (a)
40°, 50°, 60°
- (b)
60°, 60°, 60°
- (c)
50°, 50°, 50°
- (d)
60°, 70°, 70°
Select the INCORRECT statement:
- (a)
Every rectangle is a trapezium
- (b)
A quadrilateral can be drawn if all four sides and one angle is known
- (c)
Triangle is a polygon whose sum of exterior angles is double the sum of interior angles
- (d)
If diagonals of a quadrilateral are equal, it must be a rectangle.