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Class 9 Maths Part 2 Chapter 12 – Quadrilaterals | Ganita Manjari Worksheet

Practise Class 9 Maths Part 2 Chapter 12 – Quadrilaterals with this Ganita Manjari worksheet. Prepare more with important questions and revision exercises designed to strengthen understanding of quadrilaterals, improve mathematical practice and support effective preparation for class tests and examinations.

Class 9 Maths Chapter 12 Quadrilaterals Fresh Worksheet | Extra Questions
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Class 9 Maths – Chapter 12: Quadrilaterals

Fresh Worksheet – Extra Questions
Instructions:
  1. Read each question carefully.
  2. Show necessary steps for numerical and proof-based questions.
  3. Use a ruler and pencil for construction-based questions.
  4. This worksheet contains fresh questions based on the concepts of Chapter 12.
  5. The Answer Sheet is given at the end of the worksheet.

A. Basic Concepts of Quadrilaterals

Q1.
Write the definition of a quadrilateral in your own words.
Q2.
In quadrilateral ABCD, name all its sides and both its diagonals.
Q3.
In quadrilateral PQRS, identify the pair of opposite sides containing side PQ.
Q4.
How many sides, vertices, angles and diagonals does an ordinary quadrilateral have?
Q5.
A quadrilateral has three angles measuring 75°, 95° and 110°. Find its fourth angle.
Q6.
State whether the following statement is true or false: Every convex quadrilateral has all its interior angles less than 180°.
Q7.
What is the main difference between a convex quadrilateral and a non-convex quadrilateral?
Q8.
Can a self-intersecting figure be considered an ordinary quadrilateral? Give a reason.

B. Parallelograms

Q9.
In parallelogram ABCD, AB = 9 cm and BC = 6 cm. Find CD and AD.
Q10.
One angle of a parallelogram is 68°. Find all the other three angles.
Q11.
In parallelogram PQRS, ∠P = 112°. Find ∠Q, ∠R and ∠S.
Q12.
The diagonals of a parallelogram meet at O. If AO = 7 cm, find OC.
Q13.
The diagonals of parallelogram ABCD intersect at O. If BO = 8 cm, find OD.
Q14.
In a parallelogram, AC = 22 cm and BD = 16 cm. Find AO and BO, where O is the intersection point of the diagonals.
Q15.
A quadrilateral has both pairs of opposite sides equal. What can you conclude about the quadrilateral?
Q16.
A quadrilateral has one pair of opposite sides equal in length and parallel to each other. What type of quadrilateral must it be?
Q17.
The diagonals of quadrilateral ABCD bisect each other. What can you conclude about ABCD?
Q18.
One pair of opposite angles of a quadrilateral are equal. Is this condition alone enough to prove that the quadrilateral is a parallelogram? Explain briefly.
Q19.
A parallelogram has one right angle. What are the measures of all four angles?
Q20.
Complete the statement: A rectangle is a parallelogram in which __________________________.

C. Midpoint Theorem

Q21.
In triangle ABC, P and Q are the midpoints of AB and AC respectively. If BC = 18 cm, find PQ.
Q22.
In triangle PQR, X and Y are the midpoints of PQ and PR. If XY = 7 cm, find QR.
Q23.
In triangle ABC, P and Q are the midpoints of AB and AC. If AB = 12 cm and AC = 16 cm, find the lengths of AP and AQ.
Q24.
In triangle XYZ, M is the midpoint of XY. A line through M is drawn parallel to YZ and meets XZ at N. What can you say about N?
Q25.
The two parallel sides of a trapezium are 8 cm and 14 cm. Find the length of the segment joining the midpoints of its non-parallel sides.
Q26.
In triangle ABC, D and E are the midpoints of AB and AC. If BC = 20 cm, find DE and state its relation with BC.

D. Centroid

Q27.
What is a median of a triangle?
Q28.
What is the ratio in which the centroid divides each median of a triangle?
Q29.
A median of a triangle is 18 cm long. Find the distance from the vertex to the centroid and from the centroid to the midpoint of the opposite side.
Q30.
The distance from a vertex to the centroid is 12 cm. Find the length of the complete median.
Q31.
The distance from the centroid to the midpoint of a side is 5 cm. Find the distance from the opposite vertex to the centroid.

E. Varignon Parallelogram

Q32.
What figure is formed when the midpoints of all four sides of any quadrilateral are joined in order?
Q33.
The diagonals of a quadrilateral are 16 cm and 12 cm long. Find the lengths of the two different types of sides of its Varignon parallelogram.
Q34.
If the two diagonals of a quadrilateral are equal in length, what special property does its Varignon parallelogram have?
Q35.
If the diagonals of a quadrilateral are perpendicular to each other, what special type of parallelogram is formed by joining the midpoints of its sides?

F. Tiling the Plane

Q36.
Can a parallelogram be used to tile the plane without gaps or overlaps? Give a reason.
Q37.
Can every ordinary quadrilateral be used to make a tiling of the plane? State the idea used to do this.
Q38.
A regular pentagon has each interior angle equal to 108°. Can an exact number of regular pentagons meet at one point to fill 360°? Explain using calculation.
Q39.
Why is it important that tiles cover the plane without gaps and without overlapping?

G. Higher-Order Thinking Questions

Q40.
A quadrilateral has angles 72°, 108°, 72° and 108°. What special conclusion can you make if the opposite sides are also equal?
Q41.
In parallelogram ABCD, AB = 13 cm and BC = 9 cm. Find its perimeter.
Q42.
The diagonals of quadrilateral PQRS intersect at O. If PO = 6 cm, OR = 6 cm, QO = 9 cm and OS = 9 cm, what can you conclude about PQRS?
Q43.
A quadrilateral has one pair of opposite sides equal but they are not parallel. Can you conclude that it is a parallelogram? Give a reason.
Q44.
In a triangle, the midpoints of all three sides are joined. How many smaller triangles are formed? What fraction of each original side is the length of a corresponding smaller triangle side?
Q45.
A median of a triangle is 21 cm long. Find the two parts into which the centroid divides the median.
Q46.
The diagonals of a quadrilateral measure 20 cm and 18 cm. What are the lengths of the adjacent sides of its Varignon parallelogram?
Q47.
A quadrilateral has both pairs of opposite sides parallel. One side is 11 cm and an adjacent side is 7 cm. Find the lengths of all four sides.
Q48.
In parallelogram ABCD, ∠A = (3x + 10)° and ∠B = (5x – 20)°. Find x and all four angles.
Q49.
In parallelogram PQRS, ∠P = (2x + 15)° and ∠R = (4x – 25)°. Find x and the value of ∠P.
Q50.
Explain in a few steps how the midpoint theorem can help prove that the four midpoints of the sides of any quadrilateral form a parallelogram.

Answer Sheet

Answers only. Use your working in the worksheet for numerical and reasoning questions.

A. Basic Concepts

  1. A quadrilateral is a plane, non-self-intersecting closed figure made of four line segments.
  2. Sides: AB, BC, CD, DA. Diagonals: AC and BD.
  3. RS.
  4. 4 sides, 4 vertices, 4 angles and 2 diagonals.
  5. 80°.
  6. True.
  7. A convex quadrilateral has no inward indentation; all its interior angles are less than 180°. A non-convex quadrilateral has one interior angle greater than 180°.
  8. No. A self-intersecting figure does not satisfy the definition of an ordinary quadrilateral.

B. Parallelograms

  1. CD = 9 cm, AD = 6 cm.
  2. 68°, 112°, 68°, 112°.
  3. ∠Q = 68°, ∠R = 112°, ∠S = 68°.
  4. OC = 7 cm.
  5. OD = 8 cm.
  6. AO = 11 cm, BO = 8 cm.
  7. It is a parallelogram.
  8. It is a parallelogram.
  9. ABCD is a parallelogram.
  10. No. One pair of equal opposite angles alone is not sufficient.
  11. All four angles are 90°.
  12. All its angles are right angles.

C. Midpoint Theorem

  1. PQ = 9 cm.
  2. QR = 14 cm.
  3. AP = 6 cm, AQ = 8 cm.
  4. N is the midpoint of XZ.
  5. 11 cm.
  6. DE = 10 cm and DE is parallel to BC.

D. Centroid

  1. A line segment joining a vertex of a triangle to the midpoint of the opposite side.
  2. 2 : 1.
  3. Vertex to centroid = 12 cm; centroid to midpoint = 6 cm.
  4. 18 cm.
  5. 10 cm.

E. Varignon Parallelogram

  1. A parallelogram.
  2. 8 cm and 6 cm.
  3. It is a rhombus.
  4. It is a rectangle.

F. Tiling the Plane

  1. Yes. Copies of a parallelogram can cover the plane without gaps or overlaps.
  2. Yes. Suitable copies can be joined using a 180° rotation about the midpoint of a side.
  3. No. 360° ÷ 108° = 10/3, which is not a whole number.
  4. So that every point of the plane is covered exactly once, with no empty spaces or overlapping tiles.

G. Higher-Order Thinking

  1. It is a parallelogram.
  2. 44 cm.
  3. PQRS is a parallelogram.
  4. No. Equal opposite sides alone are not sufficient if they are not parallel.
  5. 4 smaller triangles; each corresponding smaller side is half the original side.
  6. Vertex to centroid = 14 cm; centroid to midpoint = 7 cm.
  7. 10 cm and 9 cm.
  8. x = 15; angles are 55°, 125°, 55°, 125°.
  9. x = 20; ∠P = 55°.
  10. Join the midpoints and apply the midpoint theorem to the two triangles formed by a diagonal. Each pair of opposite sides of the midpoint figure is parallel to the same diagonal, so the midpoint figure is a parallelogram.
Class 9 Mathematics | Chapter 12 – Quadrilaterals | Fresh Extra Practice Worksheet

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