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Quadrilaterals CBSE Class 9

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Question 1/20

Q 1. ABC is a triangle, and through A, B and C, lines are drawn parallel to BC, CA and AB, respectively, intersecting at P, Q and R. If the perimeter of PQR is 30 cm, then the perimeter of ABC is

Solution

ABC is a triangle, and through A, B and C, lines are drawn parallel to BC, CA and AB, respectively, intersecting at P, Q and R.

Perimeter of PQR is given as 30 cm.

Also, the perimeter of PQR is twice the perimeter of ABC. As ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of PQR is double the perimeter of ABC.

So, the perimeter of ABC = 30/2 = 15 cm. 

Q 2. If the diagonals of a rhombus are 14 cm and 48 cm, respectively, then its side is equal to 

Solution

The diagonals of a rhombus are perpendicular bisectors of each other. Using Pythagoras' theorem,

Q 3. Which of the following is a regular polygon with four sides? 

Solution

A square is the only regular polygon with four sides. 

Q 4. The figure formed by joining the midpoints of the adjacent sides of a parallelogram is a

Solution

The figure formed by joining the midpoints of the adjacent sides of a parallelogram is a parallelogram.

Q 5. Interior angles on the same side of a transversal are

Solution

Interior angles on the same side of a transversal are supplementary.

Q 6. A ______ is not a parallelogram. 

Solution

A trapezium is not a parallelogram. 

Q 7. The centre of a square is the point of intersection of the ____ of the square.

Solution

The centre of a square is the point of intersection of the diagonals of the square.

Q 8. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a 

Solution

If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram as well as a convex quadrilateral. 

Q 9. Which of the following is correct? 

Solution

A parallelogram whose opposite sides are equal is a rectangle, and a parallelogram whose adjacent sides are equal is a square. Angles in a rectangle and a square are 90° angles. 

Q 10. In a parallelogram ABCD, if DAB = 45° and DBC = 80°, then BDC =

Solution

  

According to the question,

DAB = DCB = 45° (opposite angles)

In DBC,

DBC + DCB + BDC = 180° 

80° + 45° + BDC = 180° 

BDC = 55° 

Q 11. In a parallelogram ABCD, ABD = 60° and BCD = 85°, then DBC is   

Solution

According to the question,

ABD = 60° = BDC (alternate angles)

In BDC,

DBC + BCD + BDC = 180° 

60° + 85° + DBC = 180° 

BDC = 35° 

Q 12. If the diagonals of a parallelogram are equal and intersect at right angles, then it is a 

Solution

If the diagonals of a parallelogram are equal and intersect at right angles, then it is a square. 

Q 13. If the adjacent sides of a parallelogram are not equal, then it is a 

Solution

If the adjacent sides of a parallelogram are not equal, then it is a rectangle. 

Q 14. Consecutive angles of a parallelogram are also called

Solution

Consecutive angles of a parallelogram are also called co-interior angles.

Q 15. Which of the following is not a parallelogram? 

Solution

A trapezium is not a parallelogram.

Q 16. If the diagonals of a parallelogram are equal, then it can be a 

Solution

If the diagonals of a parallelogram are equal, then it can be a rectangle, rhombus or square. 

Q 17. The bisectors of angles of a parallelogram form a

Solution

The bisectors of angles of a parallelogram form a rectangle.

Q 18. Which of the following quadrilaterals is not a rhombus? 

Solution

Diagonals of a rhombus are perpendicular to each other. 

Q 19. M, N and P are the midpoints of AB, AC and BC, respectively. If MN = 3 cm, NP = 4 cm and MP = 5 cm, then the measure of AC is

Solution

  

By the converse of the mid-point theorem,

MP =

2MP = AC

AC = 10 cm 

Q 20. An isosceles trapezium has 

Solution

An isosceles trapezium has one pair of opposite sides parallel and one pair of opposite sides non-parallel and equal. 

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