Hard Level Worksheet Questions
Part A: Subjective Questions
Note: Write the answers neatly on a sheet and submit them to your school subject teacher.
(1) Why can't a quadrilateral be constructed with only four angles known?
(2) Mention one real-life situation where quadrilateral construction is necessary.
(3) Which type of quadrilateral has perpendicular diagonals but unequal sides and no symmetry?
(4) How can we verify if a quadrilateral constructed with given measurements is a rhombus?
(5) Name a quadrilateral that can be constructed using two diagonals and one included angle.
(6) What property distinguishes a kite from a rhombus during construction?
(7) How many triangles are formed by the diagonals in a quadrilateral?
(8) State a condition where construction of a quadrilateral becomes impossible even if five measurements are given.
(9) Which geometric property must always be satisfied for a figure to be called a quadrilateral?
(10) If three sides and two adjacent angles are given, which vertex should you begin constructing from?
Drag each construction scenario to its correct category:
(1) Explain, with reasoning, whether a quadrilateral can be constructed if four sides and one angle between non-adjacent sides are known.
(a) Answer: Can it be constructed?
(b) Reason: Non-adjacent sides don't share a
(2) Construct rough sketch and write steps of constructing quadrilateral WXYZ where WX = 6 cm, XY = 4 cm, YZ = 5.5 cm, WZ = 5 cm, and diagonal XZ = 6.8 cm.
(a) Step 1: Draw triangle WXZ with sides WX = 6 cm, WZ = 5 cm, XZ =
(b) Step 2: From X, draw arc of radius
(c) Step 3: From Z, draw arc of radius
(d) Step 4: Mark intersection as point
(3) In quadrilateral PQRS, diagonals PR and QS intersect at O, where PR = 8 cm and QS = 6 cm. If PO = OR and QO = OS, explain what type of quadrilateral PQRS could be.
(a) Type of quadrilateral:
(b) Justification: Diagonals
(4) Write a construction strategy when two adjacent sides, one angle, and one diagonal are given.
(a) Step 1: Draw the angle at the
(b) Step 2: Mark the two adjacent sides on the
(c) Step 3: Use diagonal to locate the
(5) You are given AB = 5.6 cm, BC = 6 cm, CD = 5.4 cm, diagonal BD = 7.8 cm, and ∠ABC = 75°. Can you construct quadrilateral ABCD?
(a) Answer:
(b) Reason: Sufficient data with
(1) Construct quadrilateral GOLD where OL = 7.5 cm, LD = 6 cm, DG = 5 cm, GO = 4.5 cm and diagonal GL = 7 cm.
(2) Construct quadrilateral PLAN with PL = 6 cm, LA = 5.5 cm, AN = 6.8 cm, NP = 5.2 cm, and diagonal PA = 7.3 cm.
(a) Step 1: Draw triangle PLA with PL = 6 cm, LA = 5.5 cm, PA =
(b) Step 2: From A, draw arc of radius
(c) Step 3: From P, draw arc of radius
(d) Step 4: Mark intersection as N and complete quadrilateral
(3) Draw quadrilateral ABCD such that AB = 7.2 cm, BC = 5 cm, CD = 6 cm, DA = 4.5 cm, and diagonal AC = 8.2 cm.
(a) Step 1: Draw triangle ABC with AB = 7.2 cm, BC = 5 cm, AC =
(b) Step 2: From C, draw arc of radius
(c) Step 3: From A, draw arc of radius
(d) Justification: This ensures accuracy because we use
(4) Quadrilateral RISK is such that diagonal RK = 8.4 cm, RS = 5.6 cm, SK = 4.7 cm, angle ∠R = 70°, and angle ∠K = 95°.
(a) Step 1: Draw diagonal RK =
(b) Step 2: At R, draw angle of
(c) Step 3: Mark S at distance
(d) Step 4: At K, draw angle of
Part B: Objective Questions
1. A quadrilateral with adjacent angles 70° and 110° is likely to be:
(a) Parallelogram (b) Trapezium (c) Rhombus (d) Rectangle
Correct! Adjacent angles of 70° and 110° are supplementary, indicating a trapezium.
2. Which of the following ensures a unique construction of a quadrilateral?
(a) 2 sides and 3 angles (b) 4 angles only (c) 4 sides and 1 diagonal (d) 3 sides only
Excellent! 4 sides and 1 diagonal provide exactly 5 measurements for unique construction.
3. If diagonals are not given, what is the best approach to start quadrilateral construction?
(a) Draw angles (b) Draw longest side (c) Use compass to mark diagonals (d) Measure perpendicularly from an endpoint
Perfect! Drawing the longest side first provides a stable base for construction.
4. A quadrilateral can have one pair of sides equal and the other pair not equal. It must be a:
(a) Square (b) Trapezium (c) Rhombus (d) Rectangle
Correct! A trapezium can have one pair of parallel sides with different lengths.
5. Which of the following combinations can define a trapezium completely?
(a) 3 angles and 2 diagonals (b) 2 adjacent sides and 2 diagonals (c) 1 pair of opposite sides and 3 angles (d) 3 sides and 1 diagonal
Excellent! 3 sides and 1 diagonal provide sufficient constraints to define a trapezium uniquely.
🎉 Outstanding Achievement! You've Mastered Hard-Level Quadrilateral Construction! Here's what you conquered:
Advanced construction methods using triangular bases
Complex angle and diagonal-based constructions
Multi-step construction sequences with precise measurements
Understanding construction sufficiency and impossibility conditions
Properties of special quadrilaterals during construction
Real-world applications of quadrilateral construction principles
Strategic approaches for different given measurement combinations
Verification methods for constructed quadrilaterals
Your advanced quadrilateral construction skills prepare you for complex geometric proofs, coordinate geometry, and advanced architectural applications!