Class 8 Maths: Practical Geometry Worksheet
Practical Geometry is a crucial chapter in the Class 8 Mathematics curriculum. It focuses on the construction of geometric shapes, primarily quadrilaterals, using specific measurements such as lengths of sides, diagonals, and angles. This worksheet is designed to test student's understanding of the construction rules and their ability to draw accurate diagrams using a ruler and compass.
Key Concepts to Remember
Before attempting the questions, review the following five specific cases where a unique quadrilateral can be constructed:
- When four sides and one diagonal are given.
- When two diagonals and three sides are given.
- When two adjacent sides and three angles are given.
- When three sides and two included angles are given.
- When other special properties are known (e.g., constructing a rhombus based on its diagonals).
Part A: Theoretical Understanding
Q1. State True or False:
- A quadrilateral can be constructed uniquely if its four sides and one angle are given.
- To construct a rhombus, we need the length of its two adjacent sides only.
- A quadrilateral can be drawn if only its four angles are given.
- The diagonals of a square bisect each other at right angles.
Q2. Fill in the Blanks:
- A quadrilateral has ______ sides and ______ vertices.
- To construct a quadrilateral uniquely, a minimum of ______ independent measurements are required.
- An instrument used to draw circles and arcs is called a ______.
- If the diagonals of a quadrilateral bisect each other, it is a ______.
Q3. Short Answer Questions:
- Why is it not possible to construct a quadrilateral if only its four angles are known?
- What data is required to construct a parallelogram?
- Explain the difference between constructing a general quadrilateral and constructing a rhombus.
Part B: Practical Construction Problems
Note: For the following questions, use a ruler and compass. Read the steps carefully before drawing. Rough sketches must be drawn to plan the construction.
Topic: Constructing Quadrilaterals (4 sides and 1 diagonal)
Q4. Construct quadrilateral PQRS with PQ = 4 cm, QR = 5 cm, RS = 4.5 cm, PS = 3 cm, and diagonal PR = 6 cm.
Q5. Construct a quadrilateral JUMP with JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm, and PU = 6.5 cm.
Topic: Constructing Quadrilaterals (3 sides and 2 angles)
Q6. Construct quadrilateral MORE with MO = 6 cm, OR = 4.5 cm, M = 60, O = 105, and R = 105.
Q7. Construct quadrilateral PLAN with PL = 4 cm, LA = 6.5 cm, P = 90, A = 110, and N = 85.
Topic: Constructing Quadrilaterals (2 sides and 3 angles)
Q8. Construct a quadrilateral ABCD with AB = 5 cm, BC = 6 cm, A = 80, B = 110, and C = 70.
Topic: Special Quadrilaterals (Rhombus)
Q9. Construct a rhombus ABCD where the diagonals AC = 6.5 cm and BD = 5.5 cm.
Hint: Remember that diagonals of a rhombus bisect each other at right angles.
Topic: Special Quadrilaterals (Parallelogram)
Q10. Construct a parallelogram HEAR with HE = 5 cm, EA = 6 cm, and R = 85.
Hint: Recall that opposite sides of a parallelogram are parallel and equal, and opposite angles are equal.
Part C: Application-Based Questions
Q11. A gardener wants to build a flower bed in the shape of a quadrilateral. He has ropes of lengths 5m, 6m, 7m, and 8m. He also has a diagonal wooden plank of length 9m. Can he use these materials to mark the boundary of the flower bed? Explain which case of construction applies here.
Q12. You are given a quadrilateral BEST with BE = 4.5 cm, ES = 6 cm, ST = 5 cm. If B = 60 and E = 100, can you construct the quadrilateral? Identify the given data correctly. If data is insufficient, state what is missing.
Answer Key (Brief Hints)
Part A Solutions
Q1 (True/False):
- False (Five independent measurements are required; 4 sides + 1 angle is usually insufficient unless the angle is included between two specific sides in a specific way, but generally, 4s+1d or 3s+2a is the standard rule. Actually, 4 sides and 1 diagonal is sufficient, but 4 sides and 1 angle is not generally sufficient for a unique quadrilateral).
- True (Since all sides of a rhombus are equal, knowing one side size is enough for side lengths).
- False (Infinite quadrilaterals can have the same four angles but different side lengths).
- True.
Q2 (Fill in the Blanks):
- Four, Four
- Five
- Compass
- Parallelogram (Note: This is a sufficient condition for a parallelogram, though a rectangle, square, and rhombus fit this too).
Part B Hints
Q4 Hint: Draw triangle PQR first using SSS (PQ, QR, PR). Then locate point S using PS and RS.
Q6 Hint: Draw side MO. At M, draw a 60 angle. At O, draw a 105 angle. Mark point E on the ray from O. From R, draw an arc of 4.5 cm. Where this arc cuts the ray from M is point R.
Q9 Hint: Draw AC = 6.5 cm. Draw its perpendicular bisector. Cut off lengths of 2.75 cm (half of 5.5) on both sides of the bisector to get B and D. Join A-B, B-C, C-D, D-A.
Conclusion
Mastering Practical Geometry requires patience and precision. Regular practice with these worksheets ensures students understand the spatial properties of shapes. Always ensure your pencil is sharp and your compass is tight for the best results.
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