AP 9th Class Maths Bits Chapter 8 Quadrilaterals with Answers

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AP State Syllabus 9th Class Maths Bits 8th Lesson Quadrilaterals with Answers

Choose the correct answer :

Question 1.
The sum of the four interior angles of a quadrilateral is
A) 360 right angles
B) 4 right angles
C) 2 right angles
D) right angle
Answer:
B) 4 right angles

Question 2.
A quadrilateral in which one pair of opposite sides are parallel is a
A) parallelogram
B) kite
C) trapezium
D) rhombus
Answer:
C) trapezium

Question 3.
In the figure ∠D =

A) 110°
B) 70°
C) 60°
D) 120°
Answer:
D) 120°

Question 4.
□ABCD is a trapezium in which AB//CD. If ∠A = 45° then ∠D =

A) 45°
B) 55°
C) 135°
D) 125°
Answer:
C) 135°

Question 5.
□ABCD is a parallelogram. If ∠D = 80° then ∠A, ∠B, ∠C are
A) 80°, 100°, 100°
B) 100°, 80°, 100°
C) 80°, 100°, 80°
D) 100°, 80°, 80°
Answer:
B) 100°, 80°, 100°

Question 6.
□ABCD is a parallelogram and BC is extended. If ∠A = 40° then ∠DCE =

A) 40°
B) 140°
C) 50°
D) 60°
Answer:
A) 40°

Question 7.
The bisectors of any two interior angles of a rhombus meet at
A) accute angle
B) right angle
C) obtuse angle
D) none
Answer:
B) right angle

Question 8.
Diagonals are equal in a
A) rhombus
B) quadrilateral
C) parallelogram
D) rectangle
Answer:
D) rectangle

Question 9.
Angle between the diagonals of a rhombus is
A) acute
B) obtuse
C) right angle
D) none
Answer:
C) right angle

Question 10.
In a parallelogram ABCD, ∠BAD = 65° then ∠ADC =

A) 25°
B) 115°
C) 65°
D) 35°
Answer:
C) 65°

Question 11.
Each angle of a rectangle is
A) right angle
B) acute angle
C) obtuse angle
D) reflex angle
Answer:
A) right angle

Question 12.
In parallelogram ABCD the bisectors of ∠A and ∠B meet at ’O’. Then the value of x° is

A) 180°
B) 90°
C) 60°
D) can’t be determined
Answer:
B) 90°

Question 13.
In ΔABC, BC = 8 cm and D, E are the midpoints of AB and AC; also AF = \(\frac{1}{2}\)AD and AG = \(\frac{1}{2}\)AE then FG =

A) 4 cm
B) 32 cm
C) 3 cm
D) 2 cm
Answer:
D) 2 cm

Question 14.
In ΔABC; D, E and F are the mid points of the sides, then ΔDEF =

A) \(\frac{1}{3}\)ΔABC
B) \(\frac{1}{2}\)ΔABC
C) \(\frac{1}{4}\)ΔABC
D) 3ΔABC
Answer:
C) \(\frac{1}{4}\)ΔABC

Question 15.
If the diagonals of a quadrilateral bisect each other then it is a
A) rhombus
B) parallelogram
C) square
D) rectangle
Answer:
B) parallelogram

Question 16.
Two adjacent sides of a parallelogram are 4.7 cm and 6.3 cm then its perimeter is
A) 11 cm
B) 5.5 cm
C) 22 cm
D) 29.51 cm
Answer:
C) 22 cm

Question 17.
If each pair of opposite angles are equal then it is a
A) rectangle
B) square
C) trapezium
D) parallelogram
Answer:
D) parallelogram

Question 18.
In □ABCD; AB = DC and AD = BC also ∠A = 90° then □ABCD is a
A) rectangle
B) square
C) parallelogram
D) rhombus
Answer:
A) rectangle

Question 19.
The figure formed by joining the midpoints of sides of a rectangle is
A) square
B) rhombus
C) rectangle
D) parallelogram
Answer:
B) rhombus

Question 20.
The figure formed by joining the mid-points of sides of a rhombus is
A) rhombus
B) rectangle
C) parallelogram
D) square
Answer:
B) rectangle

Question 21.
The sum of four angles of a quadrilateral is
A) 2 right angles
B) 3 right angles
C) 4 right angles
D) 8 right angles
Answer:
C) 4 right angles

Question 22.
One of the diagonals of the quadrilateral ABCD is
A) AB
B) AC
C) BC
D) CD
Answer:
B) AC

Question 23.
The opposite vertices of the quadrilateral PQRS are
A) P, Q
B) Q, R
C) R, S
D) Q, S
Answer:
D) Q, S

Question 24.
If a parallelogram has all its angles as right angles, then it is a
A) rectangle
B) rhombus
C) square
D) trapezium
Answer:
A) rectangle

Question 25.
In a parallelogram ABCD, if ∠DAB = 50°, then ∠ABC =

A) 100°
B) 25°
C) 130°
D) 50°
Answer:
C) 130°

Question 26.
Two given sides of a parallelogram are 8 cm and 3 cm, then its perimeter is
A) 11 cm
B) 22 cm
C) 24 cm
D) 14 cm
Answer:
B) 22 cm

Question 27.
In a parallelogram, which of the following is true?
A) All sides are equal
B) Each angle is 90°
C) Diagonals are equal
D) Diagonals bisect each other
Answer:
D) Diagonals bisect each other

Question 28.
Which of the following statements is false?
A) Every parallelogram is a trapezium.
B) All trapeziums are parallelograms.
C) All parallelograms are quadrilaterals.
D) A square is a rhombus.
Answer:
B) All trapeziums are parallelograms.

Question 29.
If each pair of opposite sides of a quadrilateral is equal, then it is a
A) Parallelogram
B) Rhombus
C) Isosceles trapezium
D) Trapezium
Answer:
A) Parallelogram

Question 30.
A diagonal of a parallelogram divides it into two
A) Equal triangles
B) Similar triangles
C) Congruent triangles
D) Right triangles
Answer:
C) Congruent triangles

Question 31.
The given figure ABCD is a parallelogram. Diagonals intersect at ‘O’, then

A) ∠AOB = ∠OAB
B) ∠ACD = ∠CAB
C) OA = OB
D) ∠AOD = ∠AOB
Answer:
B) ∠ACD = ∠CAB

Question 32.
The angle bisectors of a parallelogram form a
A) Square
B) Rectangle
C) Parallelogram
D) Rhombus
Answer:
B) Rectangle

Question 33.
In the parallelogram PQRS, ∠P = 40°, then ∠R =
A) 40°
B) 50°
C) 140°
D) 80°
Answer:
A) 40°

Question 34.
The ratio of two consecutive angles of a parallelogram is 1 : 2, then the greater angle is
A) 60°
B) 30°
C) 120°
D) 150°
Answer:
C) 120°

Question 35.
ΔABC is an equilateral triangle. D, E are the mid points of AB and AC respectively. If DE = 3 cm, then the perimeter of ΔABC is

A) 9 cm
B) 12 cm
C) 15 cm
D) 18cm
Answer:
D) 18cm

Question 36.
ABCD is a parallelogram. If ∠BAD = 110°, then ∠DCE =

A) 70°
B) 55°
C) 35°
D) 60°
Answer:
A) 70°

Question 37.
In the parallelogram PQRS, \(\frac{1}{2}\)∠P + \(\frac{1}{2}\)∠Q =
A) 180°
B) 120°
C) 90°
D) 60°
Answer:
C) 90°

Question 38.
In the given figure, AC ⊥ BD and AC ≠ BD, then ABCD is a

A) Square
B) Rhombus
C) Rectangle
D) Parallelogram
Answer:
B) Rhombus

Question 39.
ABC is an equilateral triangle with side 10 cm. The perimeter of the triangle formed by joining the mid points of the sides of ΔABC is
A) 30 cm
B) 20 cm
C) 15 cm
D) 5 cm
Answer:
C) 15 cm

Question 40.
The quadrilateral in which the diagonals are equal but not perpendicular to each other is
A) Square
B) Rhombus
C) Parallelogram
D) Rectangle
Answer:
D) Rectangle

Question 41.
Statement – 1: In a parallelogram, two adjacent angles are equal then it is called Rectangle.
Statement – 2: If one angle of Rhombus is right angle then it’s square.
A) Both 1 & 2 are true
B) Both 1 & 2 are false
C) 1 is true & 2 is false
D) 1 is false & 2 is true
Answer:
A) Both 1 & 2 are true

Question 42.
If one of the angles of the quadrilateral is 120° and the remaining three angles are equal then the measure of each angle is
A) 120°
B) 80°
C) 60°
D) 40°
Answer:
B) 80°

Question 43.
Among the following the correct statement is………………
i) A Rhombus is a Square
ii) Product of two odd integers even
iii) All even numbers are composite
iv) 3 is a prime
A) i and iii
B) ii and iv
C) only ii
D) only iv
Answer:
D) only iv

Question 44.
In a Trapezium ABCD, if \(\overline{\mathbf{A B}}\) || \(\overline{\mathbf{D C}}\) and ∠D = x° then ∠A = ?
A) 180 – x°
B) 90 – x°
C) x°
D) 360 – x°
Answer:
A) 180 – x°

Question 45.
From the adjacent figure, PQ || RS, ∠RPQ = 52°, ∠RPS = 65°, ∠PSR = x° and ∠PRQ = 3y° + 5, then the value of x + y is

A) 115°
B) 137
C) 200
D) 74
Answer:
A) 115°

Question 46.
Opposite angles of a cyclic quadrilateral are………………….
A) Complimentary
B) Supplementary
C) Conjugate
D) Reflective
Answer:
B) Supplementary

Question 47.
Match the following.

A) (K, 1) (L, 2) (M, 3)
B) (K, 3) (L, 1) (M, 2)
C) (K, 2) (L, 1) (M, 3)
D) (K,3)(L, 2)(M, 1)
Answer:

Question 48.
The area of a parallelogram whose base is ‘b’ units, height is ‘h’ units (in sq. units)
A) bh
B) \(\frac{1}{2}\)bh
C) \(\frac{1}{2}\) × d₁ × d₂
D) \(\frac{1}{2}\) × h (a + b)
Answer:
A) bh

Question 49.
If the perimeters of a square and rectangle are equal, then
A) Both the areas are equal
B) Area of square is more than area of rectangle.
C) Area of rectangle is more than area of square.
D) Area of square is less than area of rectangle.
Answer:
A) Both the areas are equal

Question 50.
In a parallelogram, if one set of opposite angles are complementary, then the biggest angle in it is
A) 270°
B) 45°
C) 90°
D) 135°
Answer:
D) 135°

Question 51.
In the given figure AB || CD, AB = CD, \(\overline{\mathbf{A C}}\) and \(\overline{\mathbf{B D}}\) intersects at O. From the given information which of these is false?

A) ΔABC ≅ ΔBDC
B) ∠OBA = ∠ODC
C) ΔOAB ≅ ΔOCD
D) ‘O’ is the bisecting point of \(\overline{\mathbf{A C}}\), \(\overline{\mathbf{B D}}\)

→ Read the following information and answer the questions from 12 to 16.
Name of Quadrilateral – Properties
1. □ ABCD Only one set of opposite sides are parallel.
2. □ PQRS Diagonals bisects at each other.
3. □ KLMN All the sides and angles are qual.
Answer:
A) ΔABC ≅ ΔBDC,
D) ‘O’ is the bisecting point of \(\overline{\mathbf{A C}}\), \(\overline{\mathbf{B D}}\)

Question 52.
In □ ABCD if BC || AD, and \(\overline{\mathbf{B D}}\) is a transversal, ∠ADB = 100° – 4x°,
∠CBD = 180° – 5x°, then x° = …………………..
A) 270°
B) 80°
C) 100°
D) 180°
Answer:
B) 80°

Question 53.
In □ KLMN, KM is the diagonal, then ∠KML = ……………….
A) 180°
B) 45°
C) 90°
D) 135°
Answer:
B) 45°

Question 54.
In □ PQRS, \(\overline{\mathbf{P X}}\) and \(\overline{\mathbf{Q Y}}\) are the angle bisectors at P, ∠Q which meets at O, then ∠POQ = …………………….
A) 180°
B) 45°
C) 90°
D) 135°
Answer:
C) 90°

Question 55.
Which of the following is not correct?
A) In □ KLMN diagonals are equal
B) All the properties of □ PQRS hold good for □ KLMN
C) All the angles are equal in □ PQRS
D) All the properties of □ KLMN hold good for □ PQRS
Answer:
C) All the angles are equal in □ PQRS

Question 56.
In □ ABCD if \(\overline{\mathbf{A B}}\) || \(\overline{\mathbf{C D}}\) , then ∠A and ∠D are
A) Linear pair to each other
B) Complementary to each other
C) Supplementary to each other
D) Conjugate angles to each other
→ Read the following information and answer 17-21 :
In the parallelogram ABCD, X, Y are the mid points of \(\overline{\mathbf{C D}}\), \(\overline{\mathbf{A D}}\) respectively. Area of □ ABCD is 64 cm².

Answer:
C) Supplementary to each other

Question 57.
If AB =16 cm, then the distance between \(\overline{\mathbf{A B}}\), \(\overline{\mathbf{C D}}\) is
A) 16
B) 4
C) 8
D) 8.5
Answer:
B) 4

Question 58.
Area of Δ CYD : Area of □ ABCD is
A) 1 : 5
B) 1 : 2
C) 1 : 3
D) 1 : 4
Answer:
B) 1 : 2

Question 59.
If X and Y are joined and A and C are joined, then the area of trapezium □ XYAC Cm cm²)
A) 28
B) 4
C) 16
D) 24
Answer:
C) 16

Question 60.
In the given figure which one is wrong?
A) Area of ΔBAY = Area of ΔBCX
B) Area of ΔDAX + Area of ΔBCX = Area of ΔABX
C) Area of ΔBCY = \(\frac{1}{2}\) Area of □ ABCD
D) ΔDCY ≅ ΔBAY
Answer:
D) ΔDCY ≅ ΔBAY

Question 61.
Which of the following are in the same ratio as Area of □ ABXD : Area of □ ABCD?
A) Both Area of □ABCX: Area of □ABCD and Area of □ABCY : Area of □ABCD.
B) Area of □ABCX : Area of □ABCD
C) Area of □ABCY : Area of □ABCD
D) Area of □ABCD : Area of □BCDY
Answer:
B) Area of □ABCX : Area of □ABCD

Question 62.
In the given quadrilateral □ PQRS, PR, QS are the diagonals intersecting at ‘O’. From the given information which figure are congruent?

A) ΔORS ≅ ΔOPS
B) ΔOPQ ≅ ΔOQR
C) ΔOQR ≅ ΔORS
D) ΔPQS ≅ ΔQRS
Answer:
D) ΔPQS ≅ ΔQRS

Question 63.
From the given figure ΔKLM ≅ ΔKMN (A.S.A. rule) under CPCT ML =

A) MK
B) KL
C) MN
D) KN
Answer:
D) KN

Question 64.
From a rectangular shape of paper if you cut 3 triangles the area of biggest triangle is
A) Equal in areas
B) \(\frac{1}{4}\)^th area of rectangle
C) \(\frac{1}{2}\)^th area of rectangle
D) \(\frac{3}{4}\)^th area of rectangle
Answer:

Question 65.
In the given figure □ ABHI, □ BCDE, QACGF are parallelograms. Which among these is bigger in area?

A) All are equal
B) □ ABHI
C) □ BCDE
D) □ ACGF
Answer:
A) All are equal

Question 66.
In a rhombus a diagonal divides it into
A) Two equilateral triangles.
B) Two right angled triangles.
C) Two scalened triangles.
D) Two isosceles triangles.
Answer:
B) Two right angled triangles.

Question 67.
The opposite angles of a parallelogram are (3x – 20)° and (x + 70)° then the value of x.
A) 60°
B) 55°
C) 45°
D) 30°
Answer:
C) 45°

Question 68.
The figure formed by joining the midpoints of sides of parallelogram
A) Rhombus
B) Square
C) Parallelogram
D) Rectangle
Answer:
C) Parallelogram

Question 69.
ABCD is a parallelogram. \(\overline{\mathbf{A O}}\) and \(\overline{\mathbf{B O}}\) are bisectors of ∠A and ∠B, then ∠AOB =

A) 90°
B) 120°
C) 180°
D) 360°
Answer:
A) 90°

Question 70.
The points A, B, C and D on a circle form a quadrilateral ABCD. If ∠A = 45° then measure of ∠C =
A) 45°
B) 135°
C) 225°
D) 315°
Answer:
B) 135°

Question 71.
The side of a rhombus is 4 cm. What is its perimeter?
A) 8 cm
B) 12 cm
C) 16 cm
D) 20 cm
Answer:
C) 16 cm

Question 72.
Which of the following statement is FALSE?
A) All rectangles are parallelogram
B) All squares are parallelogram
C) All rhombus are parallelogram
D) All trapeziums are parallelogram
Answer:
D) All trapeziums are parallelogram

Question 73.
Which of the following quadrilateral satisfies the following two conditions?
i) Opposite sides are equal and adja-cent sides are unequal.
ii) Opposite angles are equal and ad-jacent angles are unequal.
A) Rectangle
B) Square
C) Parallelogram
D) Rhombus
Answer:
C) Parallelogram

Question 74.
Which of the following is TRUE?

A) P is convex & Q is convex
B) P is convex & Q is concave
C) P is concave & Q is convex
D) P is concave & Q is concave
Answer:
A) P is convex & Q is convex