1. **Problem Statement:** (a) Place two rubber bands perpendicular to each other, forming diagonals of equal length and join the ends. Identify the quadrilateral. (b) Extend one of the diagonals on both sides by 2 cm and identify the new quadrilateral. (c) Join two equilateral triangles (each side 8 cm) to form a quadrilateral. (d) Join two isosceles triangles (sides 8 cm, 8 cm, 6 cm) in different ways to form quadrilaterals. (e) Join two scalene triangles (sides 6 cm, 9 cm, 12 cm) in different ways and identify the quadrilaterals. 2. **Solution:** **Part (a): Quadrilateral from perpendicular equal diagonals** - Two rubber bands form diagonals that are equal and intersect at right angles. - The quadrilateral with diagonals equal and perpendicular is a **square** or **rhombus**. - Since diagonals are equal and perpendicular, it must be a **square**. **Part (b): Extending one diagonal by 2 cm each side** - Extending one diagonal breaks equality of diagonals. - Diagonals are no longer equal or bisect each other at right angles. - The figure becomes a **kite**, since it has two pairs of adjacent equal sides (formed by the rubber bands and extensions). **Part (c): Joining two equilateral triangles (8 cm sides)** - When joined along one side, they form a quadrilateral with all sides equal (8 cm). - This forms a **rhombus** (all sides equal, opposite sides parallel). **Part (d): Joining two isosceles triangles (8 cm, 8 cm, 6 cm)** - Joining on the equal sides (8 cm) creates a quadrilateral with sides 8 cm, 8 cm, 6 cm, 6 cm, which can look like a **kite** (two pairs of adjacent equal sides). - Joining on the base sides (6 cm) creates a trapezium-shaped quadrilateral with one pair of parallel sides. **Part (e): Joining two scalene triangles (6 cm, 9 cm, 12 cm)** - Joined in a way that two pairs of adjacent sides are equal (e.g., 6 cm and 9 cm pairs), the quadrilateral formed is a **kite**. - Other joinings may result in irregular quadrilaterals without special properties. 3. **Summary:** - Square from perpendicular, equal diagonals. - Kite from extended diagonal or adjacent side equalities. - Rhombus from joining two equilateral triangles. - Kite or trapezium from joining isosceles triangles. - Kite or irregular quadrilaterals from joining scalene triangles. **Final interpretations:** - The quadrilateral from (a) is a **square**. - The quadrilateral after extension (b) is a **kite**. - The quadrilateral from joining two equilateral triangles (c) is a **rhombus**. - Quadrilaterals from joining two isosceles triangles (d) are **kite** and **trapezium**. - Quadrilaterals from joining two scalene triangles (e) include **kite** and irregular quadrilaterals.