Case Study 1: Park Design (Parallelogram Property)
A rectangular park has opposite sides parallel and equal. The gardener noticed that ∠A = 70°.
Questions:
- In a parallelogram, opposite sides are:
(a) unequal (b) equal (c) different (d) none
Answer: (b) - ∠A + ∠B = ?
(a) 70° (b) 110° (c) 180° (d) 90°
Answer: (c) - Opposite angle of ∠A = ?
(a) 70° (b) 110° (c) 90° (d) none
Answer: (a) - Diagonals of a parallelogram:
(a) bisect each other (b) equal (c) perpendicular (d) none
Answer: (a) - Shape of the park is:
(a) Parallelogram (b) Rhombus (c) Trapezium (d) None
Answer: (a)
Case Study 2: Kite Festival (Rhombus Property)
During kite festival, a rhombus-shaped kite was made with diagonals intersecting at right angles.
Questions:
- In a rhombus, all sides are:
(a) equal (b) unequal (c) half equal (d) none
Answer: (a) - Diagonals of rhombus are:
(a) equal only (b) bisect each other only (c) perpendicular bisectors (d) none
Answer: (c) - If AC = 12 and BD = 16, then AO = ?
(a) 6 (b) 8 (c) 12 (d) none
Answer: (a) - ∠AOB = ?
(a) 60° (b) 90° (c) 120° (d) 180°
Answer: (b) - A rhombus is also a:
(a) square (b) parallelogram (c) rectangle (d) none
Answer: (b)
Case Study 3: Classroom Board (Rectangle)
A classroom board is in the shape of a rectangle. Its diagonals measure 10 cm each.
Questions:
- Diagonals of rectangle are:
(a) unequal (b) equal (c) perpendicular (d) none
Answer: (b) - If length = 6, breadth = 8, diagonal = ?
(a) 10 (b) 12 (c) 14 (d) none
Answer: (a) - Sum of all angles in rectangle = ?
(a) 180° (b) 270° (c) 360° (d) 90°
Answer: (c) - Each angle in rectangle = ?
(a) 60° (b) 90° (c) 120° (d) none
Answer: (b) - Rectangle is a special type of:
(a) parallelogram (b) rhombus (c) trapezium (d) square
Answer: (a)
Case Study 4: Diamond Ring (Square)
A diamond-shaped ring was made in the form of a square.
Questions:
- All sides are:
(a) equal (b) unequal (c) half equal (d) none
Answer: (a) - Each angle in a square = ?
(a) 45° (b) 60° (c) 90° (d) none
Answer: (c) - Diagonals of square are:
(a) equal and bisect each other (b) perpendicular (c) both (a) and (b) (d) none
Answer: (c) - If side = 7, diagonal = ?
(a) 7√2 (b) 7√3 (c) 7 (d) 14
Answer: (a) - Square is both:
(a) rhombus + rectangle (b) trapezium + kite (c) parallelogram + quadrilateral (d) none
Answer: (a)
Case Study 5: Garden Pathway (Trapezium)
A garden path is trapezium-shaped with parallel sides AB ║ CD.
Questions:
- In trapezium, how many sides parallel?
(a) 1 pair (b) 2 pairs (c) 3 pairs (d) none
Answer: (a) - Trapezium is also called:
(a) parallelogram (b) quadrilateral (c) polygon (d) both (b) and (c)
Answer: (d) - If AB ║ CD, then ∠A + ∠D = ?
(a) 90° (b) 120° (c) 180° (d) none
Answer: (c) - Special trapezium with diagonals equal is:
(a) isosceles trapezium (b) rhombus (c) square (d) none
Answer: (a) - If AB=10, CD=6, area = ?
(a) 40 (b) 32 (c) 60 (d) none
Answer: (b)
Case Study 6: Midpoint Theorem in Park
A quadrilateral garden ABCD has midpoints of AB and CD joined.
Questions:
- Midpoint theorem states:
(a) line joining midpoints ║ base (b) line bisects diagonal (c) line ⟂ base (d) none
Answer: (a) - If AB ║ DC, then line joining midpoints is:
(a) parallel to base (b) equal to half base (c) both (d) none
Answer: (c) - Midpoint theorem is used in:
(a) triangles (b) quadrilaterals (c) both (d) none
Answer: (c) - If base = 12, line joining midpoints = ?
(a) 12 (b) 6 (c) 8 (d) 10
Answer: (b) - Midpoint theorem helps in proving:
(a) parallelogram properties (b) trapezium properties (c) both (d) none
Answer: (c)
Case Study 7: Kite Shape in Decoration
A decorative piece is in the shape of a kite with diagonals 12 and 9 cm.
Questions:
- Diagonals of kite are:
(a) equal (b) unequal and perpendicular (c) bisectors only (d) none
Answer: (b) - If diagonals intersect at O, AO = ?
(a) 6 (b) 4.5 (c) 5 (d) none
Answer: (a) - Which angles are equal in a kite?
(a) two opposite angles between equal sides (b) all equal (c) right (d) none
Answer: (a) - Kite is a special:
(a) parallelogram (b) quadrilateral (c) polygon (d) both (b) and (c)
Answer: (d) - Area of kite = ½ × d₁ × d₂ = ?
(a) 27 (b) 54 (c) 108 (d) none
Answer: (b)
Case Study 8: Angles in Quadrilateral
In quadrilateral PQRS, ∠P=80°, ∠Q=95°, ∠R=85°.
Questions:
- Sum of all ∠ in quadrilateral = ?
(a) 180° (b) 270° (c) 360° (d) 540°
Answer: (c) - ∠S=?
(a) 100° (b) 110° (c) 120° (d) 90°
Answer: (a) - Property applied:
(a) angle sum property (b) Pythagoras (c) congruency (d) none
Answer: (a) - Quadrilateral with one pair parallel sides = ?
(a) trapezium (b) parallelogram (c) kite (d) none
Answer: (a) - Quadrilateral is a:
(a) polygon with 4 sides (b) polygon with 3 sides (c) polygon with 5 sides (d) none
Answer: (a)
Case Study 9: Tiles Design
A floor tile is in the shape of a parallelogram with diagonals intersecting at O.
Questions:
- Diagonals of parallelogram:
(a) equal (b) bisect each other (c) perpendicular (d) none
Answer: (b) - If AC=10, AO= ?
(a) 10 (b) 5 (c) 6 (d) none
Answer: (b) - If BD=12, BO= ?
(a) 6 (b) 12 (c) 8 (d) none
Answer: (a) - Property of diagonals proves:
(a) opposite sides equal (b) opposite angles equal (c) both (d) none
Answer: (c) - A rhombus is a parallelogram with:
(a) equal diagonals (b) equal sides (c) equal angles (d) none
Answer: (b)
Case Study 10: Playground (Square + Diagonal)
A square playground has side 14 m. Children run across the diagonal.
Questions:
- Diagonal = ?
(a) 14 (b) 14√2 (c) 28 (d) none
Answer: (b) - Diagonals of square are:
(a) equal only (b) perpendicular only (c) equal + bisect each other + ⟂ (d) none
Answer: (c) - If diagonal = 14√2, each half = ?
(a) 7√2 (b) 14 (c) 7 (d) none
Answer: (a) - Area of square = ?
(a) 196 (b) 256 (c) 280 (d) none
Answer: (a) - Square is a special case of:
(a) rectangle (b) rhombus (c) parallelogram (d) all of these
Answer: (d)