## 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 cm^{2}

B) 18 cm^{2}

C) 20 cm^{2}

D) 24 cm^{2}

Answer:

D) 24 cm^{2}

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) x^{2}

B) \(\frac{1}{2}\)(x^{2} + 5x)

C) \(\frac{1}{2}\)(2x^{2} – 5x)

D) \(\frac{1}{2}\)(2x^{2} + 5)

Answer:

B) \(\frac{1}{2}\)(x^{2} + 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