Name each of the following triangles in two different ways (you may judge the nature of the angle by observation):

(i) The triangle has sides 9 cm, 8 cm and 8 cm. Two sides are equal and all angles appear less than 90°.

∴ It is an isosceles acute-angled triangle.

(ii) The triangle has sides 13 cm, 12 cm and 5 cm. All sides are different and the angle opposite to the longest side is 90°.

Check: 5² + 12² = 25 + 144 = 169 = 13²

∴ It is a scalene right-angled triangle.

(iii) The triangle has sides 14 cm, 8 cm, 8 cm and an obtuse angle (the angle appears greater than 90°). Two sides are same and one angle is obtuse.

∴ It is an isosceles obtuse-angled triangle.

(iv) The triangle has sides 8 cm and 8 cm with the included angle 90°. Two sides are equal and one angle is right.

∴ It is an isosceles right-angled triangle.

(v) The triangle has all sides equal to 6.4 cm. All three sides are equal so all angles are 60° (acute).

∴ It is an equilateral acute-angled triangle.

(vi) The triangle has sides 11 cm, 9 cm and 17 cm. All sides are different.

Check: 9² + 11² = 81 + 121 = 202 < 17² = 289

So, the angle opposite to the longest side is obtuse.

∴ It is a scalene obtuse-angled triangle.