AP 9th Class Maths Bits 8th Lesson Quadrilaterals
Multiple Choice Questions (MCQs) :
Question 1.
What is the sum of interior angles of a parallelogram?
A) 360 degrees
B) 180 degrees
C) 270 degrees
D) 90 degrees
Answer:
A) 360 degrees
Question 2.
What type of quadrilateral is a parallelogram?
A) Square
B) Trapezoid
C) Rhombus
D) Rectangle
Answer:
B) Trapezoid
Question 3.
The diagonals of a parallelogram are _________ .
A) perpendicular
B) bisect each other
C) have equal length
D) all of the above
Answer:
B) bisect each other
Question 4.
A parallelogram with all sides equal is called a ________ .
A) Square
B) Trapezium
C) Rhombus
D) Rectangle
Answer:
C) Rhombus
Question 5.
In a parallelogram, the opposite angles are ________ .
A) Equal and parallel
B) Supplementary
C) Complementary
D) None of the above
Answer:
A) Equal and parallel
Question 6.
In a parallelogram, if one of the angles measures 60 degrees, what is the measure of the opposite angle?
A) 60 degrees
B) 120 degrees
C) 90 degrees
D) 30 degrees
Answer:
B) 120 degrees
Question 7.
The diagonals of a parallelogram bisect each other. This property is known as:
A) Opposite angles are congruent
B) Diagonals are perpendicular
C) Diagonals bisect each other
D) Opposite sides are parallel
Answer:
C) Diagonals bisect each other
Question 8.
The opposite sides of a parallelogram are
A) Congruent
B) Perpendicular
C) Parallel
D) None of the above
Answer:
C) Parallel
Question 9.
In a parallelogram, if one of the angles measures 110 degrees, what is the measure of the adjacent angle?
A) 70 degrees
B) 90 degrees
C) 80 degrees
D) 100 degrees
Answer:
C) 80 degrees
Question 10.
In a rectangle, what is the measure of each angle?
A) 45 degrees
B) 60 degrees
C) 90 degrees
D) 120 degrees
Answer:
C) 90 degrees
Question 11.
The diagonals of a rectangle are of equal length. This is because:
A) Opposite sides of a rectangle are parallel
B) Opposite sides of a rectangle are congruent
C) All angles of a rectangle are congruent
D) The diagonals of a rectangle bisect each other
Answer:
D) The diagonals of a rectangle bisect each other
Question 12.
If the length of a rectangle is 16 cm and its width is 12 cm, what is the length of its diagonal?
A) 10 cm
B) 14 cm
C) 20 cm
D) 15 cm
Answer:
C) 20 cm
Question 13.
Which of the following statements is true about a rectangle?
A) All sides are congruent
B) All angles are congruent
C) The Opposite sides are parallel and congruent
D) The diagonals are perpendicular bisectors of each other
Answer:
D) The diagonals are perpendicular bisectors of each other
Question 14.
What is the are,a of a rectangle with a length of 6 cm and a width of 4 cm?
A) 12 cm2
B) 18 cm2
C) 20 cm2
D) 24 cm2
Answer:
D) 24 cm2
Question 15.
In a rhombus, what is the measure of each angle?
A) 45 degrees
B) 60 degrees
C) 90 degrees
D) not always equal
Answer:
D) not always equal
Question 16.
Which of the following statements is true about a rhombus?
A) All sides are congruent
B) The opposite sides are parallel and congruent
C) The diagonals are perpendicular bisectors of each other
D) All above
Answer:
D) All above
Question 17.
The diagonals of a rhombus are perpendicular to each other. This is because:
A) Opposite sides of a rhombus are parallel
B) All sides of a rhombus are congruent
C) The opposite angles of a rhombus are congruent
D) The diagonals of a rhombus bisect each other
Answer:
B) All sides of a rhombus are congruent
Question 18.
What is the area of a rhombus whose diagonals are x, x + 5?
{hint A = (d1.d2)/2}
A) x2
B) \(\frac{1}{2}\)(x2 + 5x)
C) \(\frac{1}{2}\)(2x2 – 5x)
D) \(\frac{1}{2}\)(2x2 + 5)
Answer:
B) \(\frac{1}{2}\)(x2 + 5x)
Question 19.
In a square, what is the measure of each angle?
A) 45 degrees
B) 60 degrees
C) 90 degrees
D) 120 degrees
Answer:
C) 90 degrees
Question 20.
If the perimeter of a square is 40 cm, what is the length of one of its sides?
A) 5 cm
B) 8 cm
C) 10 cm
D) 12 cm
Answer:
D) 12 cm
Question 21.
How many sides does a quadrilateral have ?
A) 3
B) 5
C) 6
D) 4
Answer:
D) 4
Question 22.
How many angles are there in a quadrilateral ?
A) 4
B) 2
C) 1
D) 3
Answer:
A) 4
Question 23.
How many diagonals does a quadrilateral have ?
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2
Question 24.
How many pairs of opposite angles does a quadrilateral have ?
A) 4
B) 3
C) 2
D) 1
Answer:
C) 2
Question 25.
The sum of all the angles of a quadrilateral ?
A) 360°
B) 180°
C) 540°
D) 720°
Answer:
A) 360°
Question 26.
The three consecutive angles of a quadrilateral are 60°, 120° and 60°. The fourth angle of the quadrilateral is
A) 45°
B) 60°
C) 120°
D) none of these
Answer:
C) 120°
Question 27.
Each angle of a rectangle is
A) 90°
B) 60°
C) 45°
D) 30°
Answer:
A) 90°
Question 28.
The angle between the diagonals of a rhombus
A) 45°
B) 90°
C) 30°
D) 60°
Answer:
B) 90°
Question 29.
If one angle of a parallelogram is 90°, then the parallelogram is called a
A) kite
B) rectangle
C) rhombus
D) square
Answer:
B) rectangle
Question 30.
If in a quadrilateral, two pairs of adjacent sides are equal, then the quadrilateral is called a
A) kite
B) trapezium
C) rhombus
D) square
Answer:
A) kite
Question 31.
Which of the following is false ?
A) A square is a rectangle
B) A square is a rhombus
C) A parallelogram is a trapezium
D) A kite is a parallelogram
Answer:
D) A kite is a parallelogram
Question 32.
Which of the following is not true ?
A) A rectangle is not a square
B) A rhombus is not a square
C) A trapezium is a parallelogram
D) A kite is not a parallelogram
Answer:
C) A trapezium is a parallelogram
Question 33.
Which of the following is false ?
A) If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogrm.
B) If in a quadrilateral each pair of opposite angles is equal, then it is a parallelogrm.
C) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
D) If the sum of the consecutive interior angles of a quadrilateral is 90°, then the quadrilateral is a parallelogram.
Answer:
D) If the sum of the consecutive interior angles of a quadrilateral is 90°, then the quadrilateral is a parallelogram.
Question 34.
A quadrilateral whose all the four sides and all the four angles are equal is called a
A) rectangle
B) rhombus
C) square
D) parallelogram
Answer:
C) square
Question 35.
A quadrilateral, whose all the four sides are equal yet all the four angles are not equal, is called
A) square
B) rhombus
C) rectangle
D) parallelogram
Answer:
B) rhombus
Question 36.
If the diagonals of a parallelogram are equal and mutually perpendicular, then it will be a
A) rectangle
B) rhombus
C) trapezium
D) square
Answer:
D) square
Question 37.
ABCD is a rhombus such that ∠ABC = 40°, then ∠ADC is equal to
A) 40°
B) 45°
C) 50°
D) 20°
Answer:
A) 40°
Question 38.
In a parallelogram ABCD, if ∠A = 70°, then the measure of ∠B is
A) 10°
B) 20°
C) 110°
D) 90°
Answer:
C) 110°
Question 39.
Choose the correct statement :
A) Diagonals of a rectangle are perpendicular to each other.
B) Diagonals of a rhombus are perpendicular to each other.
C) A kite is parallelogram whose, adjacent sides are equal.
D) Diagonals of a trapezium are always equal.
Answer:
B) Diagonals of a rhombus are perpendicular to each other.
Question 40.
If a pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a
A) parallelogram
B) rectangle
C) rhombus
D) square
Answer:
A) parallelogram
Question 41.
The triangle formed by joining the midpoints of the sides of an equilateral triangle is
A) scalene
B) right
C) equilateral
D) isosceles right
Answer:
C) equilateral
Question 42.
The triangle formed by joining the midpoints of the sides of a right angled triangle is a
A) scalene
B) isosceles
C) equilateral
D) right
Answer:
D) right
Question 43.
The quadrilateral formed by joining the midpoints of the sides of a quadrilateral taken in order is a
A) kite
B) parallelogram
C) rectangle
D) square
Answer:
B) parallelogram
Question 44.
The quadrilateral formed by joining the mid-points of the sides of a rectangle taken in order is a
A) rectangle
B) square
C) rhombus
D) kite
Answer:
C) rhombus
Question 45.
The figure formed by joining the mid-points of sides of a Quadrilateral successively is _______
A) Parallelogram
B) Rhombus
C) Square
D) Rectangle
Answer:
A) Parallelogram
Assertion and Reason type questions :
Question 1.
Assertion : A rhombus is a parallelogram.
Reason : A rhombus has opposite sides that are parallel and congruent.
Answer:
Both assertion and reason are true and the reason is the correct explanation of the assertion.
Question 2.
Assertion : A square is a rhombus.
Reason : A square has four sides of equal length and opposite sides are parallel.
Answer:
Both assertion and reason are true, but the reason is not the correct explanation of the assertion.
Question 3.
Assertion : The diagonals of a rhombus are perpendicular.
Reason : The opposite angles of a rhombus are congruent.
Answer:
Both assertion and reason are true and the reason is the correct explanation of the assertion.
Question 4.
Assertion : A parallelogram with congruent diagonals is a rectangle.
Reason : A rectangle is a parallelogram with four right angles.
Answer:
Both assertion and reason are true and the reason is the correct explanation of the assertion.
Question 5.
Assertion : The diagonals of a parallelogram bisect each other.
Reason : The opposite sides of a parallelogram are parallel.
Answer:
Both assertion and reason are true and the reason is the correct explanation of the assertion.
Fill in the blanks :
1. A parallelogram is a quadrilateral with __________ pairs of parallel sides.
Answer:
2
2. The opposite sides of a parallelogram are __________ .
Answer:
Equal and parallel
3. In a parallelogram, the diagonals __________ each other.
Answer:
Bisect
4. The area of a parallelogram is given by the formula __________ .
Answer:
Base × Height
5. A parallelogram with perpendicular diagonals is a __________ .
Answer:
Rhombus
6. The diagonals of a parallelogram bisect each other __________ .
Answer:
internally
7. In a parallelogram, the opposite sides are __________ and __________ .
Answer:
equal, parallel
8. The opposite angles of a parallelogram are __________ .
Answer:
equal
9. In a parallelogram, the sum of the adjacent angles is __________ degrees.
Answer:
180
10. The diagonals of a parallelogram __________ each other.
Answer:
bisect
Match the following :
Match the geometric shape or theorem with its definition or property :
| (A) | (B) |
| 1. Rectangle | A) A quadrilateral with two pairs of parallel sides and four right angles. |
| 2. Parallelogram | B) The diagonals of a rectangle are congruent and bisect each other. |
| 3. Rhombus | C) A quadrilateral with four right angles and all four sides congruent. |
| 4. Square | D) A quadrilateral with opposite sides parallel and congruent. |
| 5. Opposite sides | E) A line segment that joins the midpoint of two sides of a triangle. |
| 6. Opposite angles | F) A line segment that connects the midpoints of two sides of a triangle. |
| 7. Diagonal | G) A line segment that connects two non-adjacent vertices of a polygon. |
| 8. Midpoint Theorem | H) The midpoint of a line segment joining two sides of a triangle is parallel to the third side and half its length. |
| 9. Rhombus Property | I) The opposite sides of a parallelogram are congruent. |
| 10. Rectangle Property | J) A quadrilateral with four congruent angles and sides. |
Answer:
1 – A, 2 – D, 3 – C, 4 – J, 5 – F, 6 – E, 7 – G, 8 – H 9 – I 10 – B
| (A) | (B) |
| 1. Rectangle | A) A quadrilateral with two pairs of parallel sides and four right angles. |
| 2. Parallelogram | D) A quadrilateral with opposite sides parallel and congruent. |
| 3. Rhombus | C) A quadrilateral with four right angles and all four sides congruent. |
| 4. Square | J) A quadrilateral with four congruent angles and sides. |
| 5. Opposite sides | F) A line segment that connects the midpoints of two sides of a triangle. |
| 6. Opposite angles | E) A line segment that joins the midpoint of two sides of a triangle. |
| 7. Diagonal | G) A line segment that connects two non-adjacent vertices of a polygon. |
| 8. Midpoint Theorem | H) The midpoint of a line segment joining two sides of a triangle is parallel to the third side and half its length. |
| 9. Rhombus Property | I) The opposite sides of a parallelogram are congruent. |
| 10. Rectangle Property | B) The diagonals of a rectangle are congruent and bisect each other. |
Explanations:
1. A rectangle is a quadrilateral with two pairs of parallel sides and four right angles.
2. A parallelogram is a quadrilateral with opposite sides parallel and congruent.
3. A rhombus is a quadrilateral with four right angles and all four sides congruent.
4. A square is a quadrilateral with four congruent angles and sides.
5. The mid-segment is a line segment that connects the midpoints of two sides of a triangle.
6. The median is a line segment that joins the midpoint of two sides of a triangle.
7. A diagonal is a line segment that connects two non-adjacent vertices of a polygon.
8. The midpoint theorem states that the midpoint of a line segment joining two sides of a triangle is parallel to the third side and half its length.
9. The rhombus property states that the opposite sides of a rhombus are parallel and congruent.
10. The rectangle property states that the diagonal^ of a rectangle are congruent and bisect