Chapter 5. Understanding Quadrilaterals and Practical Geometry

Choose the correct Answers:

1: The number of diagonals in a polygon of n sides is
(a) n(n-1)2           (b) n(n-2)2                      (c) n(n-3)2                    (d) n (n–3).
Ans: (c).
2: The angles of a quadrilateral ABCD taken in an order are in the ratio 3 : 7 : 6 : 4. Then ABCD is a
(a) kite(b)parallelogram
(c) rhombus(d)trapezium
Ans: (d)

3: If the diagonals of a quadrilateral bisect each other at right angles, it will be a
(a)rhombus(b)trapezium
(c)rectangle(d)kite
Ans: (a).
4: The sum of the angles of a quadrilateral is
(a)180°         (b)270°     (c)360°     (d)300°
Ans (c).
5:In a square ABCD, the diagonals meet at point O. The ∆AOB is
(a) isosceles righttriangle
(b) equilateral triangle
(c) isosceles triangle but not right triangle
(d) scalene right triangle.
Ans: (a).

6: ABCD is a quadrilateral in which AB = 5 cm, CD = 8 cm and the sum of angle A and angle D is 180°. What is the name of this quadrilateral?
(a)Parallelogram            (b)Trapezium
(c)Rhombus                   (d)Can not be determined
Ans: (b).
7:Rukmini has a farm land which is triangular in shape. What is the sum of all the exterior angles taken in an order of the farm land?
(a) 90°      (b) 180°            (c) 360°      (d) Can not be determined.
Ans: (c).
8: How many sides does an octagon have?
(A)7         (b) 8           (c)  9              (d) 10
Ans: (b)

9: If three angles of a quadrilateral are each equal to 75°, the fourth angle is
(a) 150°     (b)135°         (c)45°      (d)75°
10: For which of the following, diagonals bisect each other?
(a) Square            (b) Kite          (c) Trapezium           (d) Quadrilateral
11. For which of the following figures, all angles are equal?
(a) Rectangle           (b) Kite
(c) Trapezium         (d) Rhombus
12: For which of the following figures, diagonals are perpendicular to each other?
(a) Parallelogram(b) Kite
(c) Trapezium(d) Rectangle
13:  For which of the following figures, diagonals are equal?
(a) Trapezium(b) Rhombus
(c) Parallelogram(d) Rectangle.

14.Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.     Photo

(a) P(b) Q(c) R(d) S

15.Which of the following figures satisfy the following property?
- Only one pair of sides are parallel. 

Photo

16.Which of the following figures do not satisfy any of the following properties?
- All sides are equal.
- All angles are right angles.
- Opposite sides are parallel.    (Photo)

17. Which of the following properties describe a trapezium?
(a) A pair of opposite sides is parallel.

(b) The diagonals bisect each other.
(c) The diagonals are perpendicular to each other.
(d) The diagonals are equal.
18.Which of the following is a property of a parallelogram?
(a) Opposite sides are parallel.
(b) The diagonals bisect each other at right angles.
(c) The diagonals are perpendicular to each other.
(d) All angles are equal.
19.What is the maximum number of obtuse angles that a quadrilateral can have ?
(a) 1(b) 2(c) 3(d) 4
20.How many non-overlapping triangles can we make in a n-gon (polygon having n sides), by joining the vertices?
(a) n –1       (b) n –2            (c) n –3          (d) n –4
21.What is the sum of all the angles of a pentagon?
(a) 180°(b) 360°(c) 540°(d) 720°

22.What is the sum of all angles of a hexagon?
(a) 180°(b) 360°(c) 540°(d) 720°
23.If two adjacent angles of a parallelogram are (5x – 5)° and (10x +35)°, then the ratio of these angles is
(a) 1 : 3        (b) 2 : 3         (c) 1 : 4         (d) 1 : 2
24.A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a __________.
(a) rhombus       (b) parallelogram             (c) square     (d) rectangle
25.A quadrilateral whose opposite sides and all the angles are equal is a
(a) rectangle(b) parallelogram(c) square (d) rhombus
26.A quadrilateral whose all sides, diagonals and angles are equal is a
(a) square(b) trapezium(c) rectangle(d) rhombus.

27.How many diagonals does a hexagon have?
(a) 9            (b) 8           (c) 2        (d)6
28.If the adjacent sides of a parallelogram are equal then parallelogram is a
(a) rectangle(b) trapezium(c) rhombus(d)square
29.If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a
(a) rhombus(b) rectangle(c) square(d) parallelogram
30.The sum of all exterior angles of a triangle is
(a) 180°        (b) 360°         (c) 540°         (d) 720°
31.Which of the following is an equiangular and equilateral polygon?
(a) Square         (b) Rectangle        (c) Rhombus     (d) Right triangle
32.Which one has all the properties of a kite and a parallelogram?
(a) Trapezium(b) Rhombus(c) Rectangle(d) Parallelogram
33.The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is
(a) 72°(b) 144°(c) 36°(d) 18°

34.In the trapezium ABCD, the measure of ∠D is
(a) 55°(b) 115°(c) 135°(d) 125°

(Photo )
35.A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is
(a) 150°(b) 120°(c) 105°(d) 140°
36.The number of sides of a regular polygon where each exterior angle has a measure of 45° is
(a) 8(b) 10(c) 4(d) 6

37.In a parallelogram PQRS, if ∠P = 60°, then other three angles are
(a) 45°, 135°, 120°(b) 60°, 120°, 120°
(c) 60°, 135°, 135°(d) 45°, 135°, 135°
38.If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are
(a) 72°, 108°(b) 36°, 54°(c) 80°, 120°(d) 96°, 144°
39.If PQRS is a parallelogram, then ∠P – ∠R is equal to
(a) 60°(b) 90°(c) 80°(d) 0°
40.The sum of adjacent angles of a parallelogram is
(a) 180°(b) 120°(c) 360°(d) 90°
41.The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is
(a) 100°(b) 150°(c) 105°(d) 120°
42.In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC =
(a) 60°          (b) 30°            (c) 150°           (d) 120°

Photo

43.Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is
(a) 25 cm(b) 20 cm(c) 26 cm(d) 3.5 cm
44.If the adjacent angles of a parallelogram are equal, then the parallelogram is a
(a) rectangle            (b) trapezium
(c) rhombus             (d) any of the three
45.Which of the following can be four interior angles of a quadrilateral?
(a) 140°, 40°, 20°, 160°(b) 270°, 150°, 30°, 20°
(c) 40°, 70°, 90°, 60°(d) 110°, 40°, 30°, 180°

46.The sum of angles of a concave quadrilateral is
(a) more than 360°           (b) less than 360°
(c) equal to 360°               (d) twice of 360°
47.Which of the following can never be the measure of exterior angle of a regular polygon?
(a) 22°(b) 36°(c) 45°(d) 30°
48.In the figure, BEST is a rhombus, Then the value of y – x is
(a) 40°(b) 50°(c) 20°(d) 10°

Photo
49.The closed curve which is also a polygon is

Photo

50.Which of the following is not true for an exterior angle of a regular polygon with n sides?
(a) Each exterior angle =360°n
(b) Exterior angle = 180° – interior angle
(c) n=360°exterior angle
(d) Each exterior angle =n-2×180°n
51.PQRS is a square. PR and SQ intersect at O. Then ∠POQ is a
(a) Right angle           (b) Straight angle
(c) Reflex angle         (d) Complete angle

52.Two adjacent angles of a parallelogram are in the ratio 1:5. Then all the angles of the parallelogram are
(a) 30°, 150°, 30°, 150°               (b) 85°, 95°, 85°, 95°
(c) 45°, 135°, 45°, 135°               (d) 30°, 180°, 30°, 180°
53.A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90°. Then PQRS is a
(a) square           (b) rectangle         (c) rhombus            (d) trapezium
54.The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a
(a) parallelogram                               (b) trapezium with PQ || RS
(c) trapezium with QR||PS              (d) kite
55.PQRS is a trapezium in which PQ||SR and ∠P=130°, ∠Q=110°. Then ∠R is equal to:
(a) 70°     (b) 50°      (c) 65°        (d) 55°
56.The number of sides of a regular polygon whose each interior angle is of 135° is
(a) 6         (b) 7         (c) 8         (d) 9
57.If a diagonal of a quadrilateral bisects both the angles, then it is a
(a) kite                        (b) parallelogram
(c) rhombus               (d) rectangle
58.To construct a unique parallelogram, the minimum number of measurements required is
(a) 2          (b) 3          (c) 4         (d) 5
59.To construct a unique rectangle, the minimum number of measurements required is
(a) 4           (b) 3               (c) 2           (d) 1
 Fill in the blanks
53.In quadrilateral HOPE, the pairs of opposite sides are __________.
54.In quadrilateral ROPE, the pairs of adjacent angles are __________.
55.In quadrilateral WXYZ, the pairs of opposite angles are __________.

56.The diagonals of the quadrilateral DEFG are __________ and__________.
57.The sum of all __________ of a quadrilateral is 360°.
58.The measure of each exterior angle of a regular pentagon is __________.
59.Sum of the angles of a hexagon is __________.
60.The measure of each exterior angle of a regular polygon of 18 sides is __________.
61.The number of sides of a regular polygon, where each exterior angle has a measure of 36°, is __________.
62. (Photo)  is a closed curve entirely made up of line segments. The another name for this shape is __________.
63.A quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure is __________.
64.The measure of each angle of a regular pentagon is __________.
65.The name of three-sided regular polygon is __________.
66.The number of diagonals in a hexagon is __________.
67.A polygon is a simple closed curve made up of only __________.

68.A regular polygon is a polygon whose all sides are equal and all __________ are equal.
69.The sum of interior angles of a polygon of n sides is __________right angles.
70.The sum of all exterior angles of a polygon is __________.
71.__________ is a regular quadrilateral.
72.A quadrilateral in which a pair of opposite sides is parallel is __________.
73.If all sides of a quadrilateral are equal, it is a __________.
74.In a rhombus diagonals intersect at __________ angles.
75. __________ measurements can determine a quadrilateral uniquely.

6.A quadrilateral can be constructed uniquely if its three sides and __________ angles are given.
77.A rhombus is a parallelogram in which __________ sides are equal.
78.The measure of __________ angle of concave quadrilateral is more than 180°.
79.A diagonal of a quadrilateral is a line segment that joins two __________vertices of the quadrilateral.
80.The number of sides in a regular polygon having measure of an exterior angle as 72° is __________.
81.If the diagonals of a quadrilateral bisect each other, it is a __________.
82.The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is __________.
83.A nonagon has __________ sides.
84.Diagonals of a rectangle are __________.
85.A polygon having 10 sides is known as __________.
86.A rectangle whose adjacent sides are equal becomes a __________.

87.If one diagonal of a rectangle is 6 cm long, length of the other diagonal is __________.
88.Adjacent angles of a parallelogram are __________.
89.If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as __________.
90.In trapezium ABCD with AB||CD, if ∠A = 100°, then ∠D = __________.
91.The polygon in which sum of all exterior angles is equal to the sum of interior angles is called __________.

92: The diagonals of a rhombus bisect each other at _____ angles.
Ans: Right.
93: For getting diagonals through vertex A of a pentagon ABCDE, A is joined to _________.
Ans: C and D.
94: For constructing a unique quadrilateral at least __________ measurements are required.
Ans:    Five.
95: If diagonals of a quadrilateral bisect at right angles it is a __________.
Ans: Rhombus (or square).
96: The diagonals of a __________ intersect at right angles.
Ans:  Kite.