Let's analyze each triangle and determine its type in two different ways:

1. (i) ∆XYZ with ∠Z = 90°

   • Type 1: Right-angled triangle (since it has a 90° angle).
   • Type 2: Scalene triangle (assuming the sides are all different).

2. (ii) ∆PQR such that PQ = QR = PR = 5 cm

   • Type 1: Equilateral triangle (all sides are equal).
   • Type 2: Acute-angled triangle (all angles are less than 90°, and in an equilateral triangle, each angle is 60°).

3. (iii) Triangle with lengths of sides 7 cm, 8 cm, and 9 cm

   • Type 1: Scalene triangle (all sides are different).
   • Type 2: Acute-angled triangle (since the square of the longest side is less than the sum of the squares of the other two sides, meaning all angles are less than 90°).

Would you like more details or have any questions?

Here are five related questions for further practice:

1. What is the definition of an obtuse-angled triangle?
2. How can you classify triangles based on their angles?
3. Can a scalene triangle ever be equilateral?
4. What is the Pythagorean theorem, and how does it apply to right-angled triangles?
5. How do you determine if a triangle is acute, obtuse, or right-angled using side lengths?

Tip: For any triangle, you can classify it based on its angles (acute, right, obtuse) and its sides (scalene, isosceles, equilateral).